Bell's theorem - Knowledge

6723: 13624: 6652:, and deterministic, because it consists of the unitary part of quantum mechanics without collapse. It can generate correlations that violate a Bell inequality because it violates an implicit assumption by Bell that measurements have a single outcome. In fact, Bell's theorem can be proven in the Many-Worlds framework from the assumption that a measurement has a single outcome. Therefore, a violation of a Bell inequality can be interpreted as a demonstration that measurements have multiple outcomes. 6495: 112:, have been performed many times since. Often, these experiments have had the goal of "closing loopholes", that is, ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests. Bell tests have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments are incompatible with any local hidden-variable theory. 13614: 12739: 2296: 2103: 6105:

out, obtaining a measurement outcome on one half of an entangled pair implies certainty about the outcome of a corresponding measurement on the other half. The "EPR criterion of reality" posits that because the second half of the pair was not disturbed, that certainty must be due to a physical property belonging to it. In other words, by this criterion, a hidden variable

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is true from the point of view of each copy of Bob. They will obtain a mutually well-defined result only when their future light cones overlap. At this point we can say that the Bell correlation starts existing, but it was produced by a purely local mechanism. Therefore, the violation of a Bell inequality cannot be interpreted as a proof of non-locality.

6472:, in fact paying the authors who published there at the time. Because the journal did not provide free reprints of articles for the authors to distribute, however, Bell had to spend the money he received to buy copies that he could send to other physicists. While the articles printed in the journal themselves listed the publication's name simply as 1899: 87:. Bell deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. Such a constraint would later be named a 2258: 6285:

that starts with the premise of local, discretized degrees of freedom and then imposes a "knowledge balance principle" that restricts how much an observer can know about those degrees of freedom, thereby making them into hidden variables. The allowed states of knowledge ("epistemic states") about the

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There are many variations on the basic idea, some employing stronger mathematical assumptions than others. Significantly, Bell-type theorems do not refer to any particular theory of local hidden variables, but instead show that quantum physics violates general assumptions behind classical pictures of

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must exist within the second, as-yet unmeasured half of the pair. No contradiction arises if only one measurement on the first half is considered. However, if the observer has a choice of multiple possible measurements, and the vectors defining those measurements form a Kochen–Specker configuration,

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The explanation it provides for the Bell correlations is that when Alice and Bob make their measurements, they split into local branches. From the point of view of each copy of Alice, there are multiple copies of Bob experiencing different results, so Bob cannot have a definite result, and the same

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were produced traveling in opposite directions, and came to the conclusion that hidden variables could not explain the correlations that could be obtained in such situations. However, complications arose due to the fact that kaons decay, and he did not go so far as to deduce a Bell-type inequality.

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writes that "no experiment ... can be said to be totally loophole-free," but he says the experiments "remove the last doubts that we should renounce" local hidden variables, and refers to examples of remaining loopholes as being "far fetched" and "foreign to the usual way of reasoning in physics."

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stand in widely separated locations. Their colleague Victor prepares a pair of particles and sends one to Alice and the other to Bob. When Alice receives her particle, she chooses to perform one of two possible measurements (perhaps by flipping a coin to decide which). Denote these measurements by

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Prior to proving his 1964 result, Bell also proved a result equivalent to the Kochen–Specker theorem (hence the latter is sometimes also known as the Bell–Kochen–Specker or Bell–KS theorem). However, publication of this theorem was inadvertently delayed until 1966. In that paper, Bell argued that

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The Kochen–Specker type of argument, using configurations of interlocking bases, can be combined with the idea of measuring entangled pairs that underlies Bell-type inequalities. This was noted beginning in the 1970s by Kochen, Heywood and Redhead, Stairs, and Brown and Svetlichny. As EPR pointed

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loopholes. The detection loophole is opened when a small fraction of the particles (usually photons) are detected in the experiment, making it possible to explain the data with local hidden variables by assuming that the detected particles are an unrepresentative sample. The locality loophole is

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provided an argument that a broad class of hidden-variable theories are incompatible with quantum mechanics. More specifically, Gleason's theorem rules out hidden-variable models that are "noncontextual". Any hidden-variable model for quantum mechanics must, in order to avoid the implications of

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of quantum mechanics, which requires that all particles in the universe be able to instantaneously exchange information with all others. One challenge for non-local hidden variable theories is to explain why this instantaneous communication can exist at the level of the hidden variables, but it

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Gleason's theorem, involve hidden variables that are not properties belonging to the measured system alone but also dependent upon the external context in which the measurement is made. This type of dependence is often seen as contrived or undesirable; in some settings, it is inconsistent with

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Bell's 1964 theorem requires the possibility of perfect anti-correlations: the ability to make a probability-1 prediction about the result from the second detector, knowing the result from the first. This is related to the "EPR criterion of reality", a concept introduced in the 1935 paper by

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Reactions to Bell's theorem have been many and varied. Maximilian Schlosshauer, Johannes Kofler, and Zeilinger write that Bell inequalities provide "a wonderful example of how we can have a rigorous theoretical result tested by numerous experiments, and yet disagree about the implications."

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The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a two-channel polariser whose orientation (a or b) can be set by the experimenter. Emerging signals from each channel are detected and coincidences of four types (++, −−, +− and −+) counted by the

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to remove this limitation. This began a trend of progressively more stringent Bell tests. The GHZ thought experiment was implemented in practice, using entangled triplets of photons, in 2000. By 2002, testing the CHSH inequality was feasible in undergraduate laboratory courses.

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Einstein, Podolsky, and Rosen. This paper posits: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

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As Bell pointed out, some predictions of quantum mechanics can be replicated in local hidden-variable models, including special cases of correlations produced from entanglement. This topic has been studied systematically in the years since Bell's theorem. In 1989,

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trial can measure this quantity, because Alice and Bob can only choose one measurement each, but on the assumption that the underlying properties exist, the average value of the sum is just the sum of the averages for each term. Using angle brackets to denote

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Although both the locality and detection loopholes had been closed in different experiments, a long-standing challenge was to close both simultaneously in the same experiment. This was finally achieved in three experiments in 2015. Regarding these results,

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In Bell tests, there may be problems of experimental design or set-up that affect the validity of the experimental findings. These problems are often referred to as "loopholes". The purpose of the experiment is to test whether nature can be described by

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had grown interested in the foundations of quantum physics, and in 1957 he drew up a list of postulates that he took to be a precise definition of quantum mechanics. Mackey conjectured that one of the postulates was redundant, and shortly thereafter,

2098:{\displaystyle \langle A_{0}\otimes B_{0}\rangle ={\frac {1}{\sqrt {2}}},\langle A_{0}\otimes B_{1}\rangle ={\frac {1}{\sqrt {2}}},\langle A_{1}\otimes B_{0}\rangle ={\frac {1}{\sqrt {2}}},\langle A_{1}\otimes B_{1}\rangle =-{\frac {1}{\sqrt {2}}}\,.} 7163:. In a deterministic hidden-variable theory, there exists an underlying physical property that fixes the result found in the measurement. Conditional on the value of the underlying physical property, any given outcome (for example, a result of 1767: 6562:, making it possible for the result of one measurement to influence the other without contradicting relativity. In some experiments there may be additional defects that make local-hidden-variable explanations of Bell test violations possible. 701: 3773: 6809:

We are for convenience assuming that the response of the detector to the underlying property is deterministic. This assumption can be replaced; it is equivalent to postulating a joint probability distribution over all the observables of the

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Bell's 1964 paper points out that under restricted conditions, local hidden-variable models can reproduce the predictions of quantum mechanics. He then demonstrates that this cannot hold true in general. Bell considers a refinement by

4035: 2567:. Alice and Bob can agree upon any strategy they desire before the game, but they cannot communicate once the game begins. In any theory based on local hidden variables, Alice and Bob's probability of winning is no greater than 6275: 4897:

measurement upon Charlie's qubit. Indeed, this same logic applies to both measurements and all three qubits. Per the EPR criterion of reality, then, each particle contains an "instruction set" that determines the outcome of a

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Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables. They are ready to give up locality, explaining the violation of Bell's inequality by means of a non-local

7183:) must be either impossible or guaranteed. But Gleason's theorem implies that there can be no such deterministic probability measure, because it proves that any probability measure must take the form of a mapping 6408:

described by a joint wave function. However, the EPR paper adds the idea later known as the EPR criterion of reality, according to which the ability to predict with probability 1 the outcome of a measurement upon

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gives the sum of the average values that Victor expects to find across multiple trials. This value exceeds the classical upper bound of 2 that was deduced from the hypothesis of local hidden variables. The value

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took the message of Bell's theorem to be that, because the premise of locality is physically reasonable, "hidden variables cannot be introduced without abandoning some of the results of quantum mechanics".

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Aspect, A.; Grangier, P. (1985). "About resonant scattering and other hypothetical effects in the Orsay atomic-cascade experiment tests of Bell inequalities: a discussion and some new experimental data".

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A necessary assumption to derive Bell's theorem is that the hidden variables are not correlated with the measurement settings. This assumption has been justified on the grounds that the experimenter has

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proposed a variant of the EPR thought experiment in which the measurements have discrete ranges of possible outcomes, unlike the position and momentum measurements considered by EPR. The year before,

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This thought experiment can also be recast as a traditional Bell inequality or, equivalently, as a nonlocal game in the same spirit as the CHSH game. In it, Alice, Bob, and Charlie receive bits

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represent measurements that can be performed upon a system having that Hilbert space. Each vector in a basis represents a possible outcome of that measurement. Suppose that a hidden variable

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it may be concluded that the ψ function is not unambiguously coordinated with the physical condition. This coordination of several ψ functions with the same physical condition of system

6176:, joint quantum states for a pair of systems that yield EPR-type correlations but also admit a hidden-variable model. Werner states are bipartite quantum states that are invariant under 3922: 2974: 512: 3628: 3083: 132:

nature. The original theorem proved by Bell in 1964 is not the most amenable to experiment, and it is convenient to introduce the genre of Bell-type inequalities with a later example.

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and Irving Shaknov had successfully measured polarizations of photons produced in entangled pairs, thereby making the Bohm version of the EPR thought experiment practically feasible.

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Gröblacher, Simon; Paterek, Tomasz; Kaltenbaek, Rainer; Brukner, Časlav; Żukowski, Marek; Aspelmeyer, Markus; Zeilinger, Anton (2007). "An experimental test of non-local realism".

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because an explanation of quantum phenomena in terms of hidden variables would require nonlocality, the EPR paradox "is resolved in the way which Einstein would have liked least."

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argues for the rejection of hidden variables and concludes that "quantum mechanics is probably as realistic as any theory of its scope and maturity ever will be". Likewise,

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when taken as belonging to another. In other words, a Kochen–Specker configuration is an "uncolorable set" that demonstrates the inconsistency of assuming a hidden variable

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would go on to perform a Bell test in 1972. This was only a limited test, because the choice of detector settings was made before the photons had left the source. In 1982,

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Bell posited that a local hidden-variable model for these correlations would explain them in terms of an integral over the possible values of some hidden parameter

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cannot be used to send signals. A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories, though not Bohmian mechanics itself.

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Pan, Jian-Wei; Bouwmeester, D.; Daniell, M.; Weinfurter, H.; Zeilinger, A. (2000). "Experimental test of quantum nonlocality in three-photon GHZ entanglement".

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Experimental results contradict the classical curves and match the curve predicted by quantum mechanics as long as experimental shortcomings are accounted for.

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presented what he claimed to be a proof that there could be no "hidden parameters". The validity and definitiveness of von Neumann's proof were questioned by

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of the Einstein–Podolsky–Rosen (EPR) thought experiment. In this scenario, a pair of particles are formed together in such a way that they are described by a

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Fry, E. S.; Walther, T. (2002). "Atom based tests of the Bell Inequalities — the legacy of John Bell continues". In Bertlmann, R. A.; Zeilinger, A. (eds.).

2595:, regardless of what strategy they agree upon beforehand. However, if they share an entangled quantum state, their probability of winning can be as large as 4040: 2784: 6449:. The Kochen–Specker theorem refines this statement by constructing a specific finite subset of rays on which no such probability measure can be defined. 6286:

underlying variables ("ontic states") mimic some features of quantum states. Correlations in the toy model can emulate some aspects of entanglement, like

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then simplified to use only three particles. In this thought experiment, Victor generates a set of three spin-1/2 particles described by the quantum state

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Gerhardt, I.; Liu, Q.; Lamas-Linares, A.; Skaar, J.; Scarani, V.; et al. (2011). "Experimentally faking the violation of Bell's inequalities".

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Barnum, H.; Beigi, S.; Boixo, S.; Elliott, M. B.; Wehner, S. (2010-04-06). "Local Quantum Measurement and No-Signaling Imply Quantum Correlations".

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A Kochen–Specker configuration is a finite set of vectors made of multiple interlocking bases, with the property that a vector in it will always be

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An illustration of the CHSH game: the referee, Victor, sends a bit each to Alice and to Bob, and Alice and Bob each send a bit back to the referee.

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Einstein argued persistently that quantum mechanics could not be a complete theory. His preferred argument relied on a principle of locality:

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Matsukevich, D. N.; Maunz, P.; Moehring, D. L.; Olmschenk, S.; Monroe, C. (2008). "Bell Inequality Violation with Two Remote Atomic Qubits".

9537: 8156: 6314: 11172: 10995:"The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning" 13505: 7492: 6364:

from the measurements made, and from the ψ function of the total system. This determination, however, gives a result which depends upon

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Hensen, B.; et al. (21 October 2015). "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres".

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is the projector onto its associated eigenspace. For the purposes of this discussion, we can take the eigenvalues to be non-degenerate.

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will furnish the ψ function after their interaction has taken place. Let us now determine the physical condition of the partial system

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Dehlinger, Dietrich; Mitchell, M. W. (2002). "Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory".

2669:, a measuring instrument that can be oriented in different directions and that reports one of two possible outcomes, representable by 1258:{\displaystyle |\langle A_{0}B_{0}\rangle +\langle A_{0}B_{1}\rangle +\langle A_{1}B_{0}\rangle -\langle A_{1}B_{1}\rangle |\leq 2\,.} 6899:

acting on the Hilbert space. When an observable is measured, the result will be one of its eigenvalues with probability given by the

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after the interaction and which can reasonably not be considered as dependent on the particular measurement we perform on the system

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The question of whether quantum mechanics can be "completed" by hidden variables dates to the early years of quantum theory. In his

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be explained in terms of hidden variables, then proceeds to show that the full range of possibilities involving intermediate angles

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The exact nature of the assumptions required to prove a Bell-type constraint on correlations has been debated by physicists and by

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as completely as possible by measurements. Then the quantum mechanics allows us to determine the ψ function of the partial system

2665:(which is an example of an entangled state). The particles then move apart in opposite directions. Each particle is measured by a 13293: 12719: 11237: 7103:

atom will report that the atom's angular momentum along the chosen axis is one of three possible values, which can be designated

5464:{\displaystyle (a_{x}b_{y}c_{y})(a_{y}b_{x}c_{y})(a_{y}b_{y}c_{x})=a_{x}b_{x}c_{x}a_{y}^{2}b_{y}^{2}c_{y}^{2}=a_{x}b_{x}c_{x}\,,} 4870:

measurement. According to the EPR criterion of reality, there would be an "element of reality" corresponding to the outcome of a

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Werner, Reinhard F. (1989-10-01). "Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model".

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which have interaction with each other only during limited time. Let the ψ function before their interaction be given. Then the

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Suppose that each measurement reveals a property that the particle already possessed. For instance, if Alice chooses to measure

13658: 12403: 11961: 10789:; Timpson, Christopher G. (2016). "Bell on Bell's Theorem: The Changing Face of Nonlocality". In Bell, Mary; Gao, Shan (eds.). 9374: 7812: 6478: 10940: 4374:. Victor then sends a particle each to Alice, Bob, and Charlie, who wait at widely separated locations. Alice measures either 4090:

Therefore, there is no local hidden-variable model that can reproduce the predictions of quantum mechanics for all choices of

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shows again that the ψ function cannot be interpreted as a (complete) description of a physical condition of a unit system.

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However, it is easy to find situations where quantum mechanics violates the Bell inequality. For example, let the vectors

3625:. Bell proves that the difference in correlation between these two choices of detector setting must satisfy the inequality 13575: 11920: 10757: 10279:

Giustina, M.; et al. (16 December 2015). "Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons".

9446: 8085: 7462: 1885:{\displaystyle B_{0}=-{\frac {\sigma _{x}+\sigma _{z}}{\sqrt {2}}},\ B_{1}={\frac {\sigma _{x}-\sigma _{z}}{\sqrt {2}}}.} 1356:); and second, that Alice's choice of action cannot influence Bob's result or vice versa (often called the assumption of 120: 6574:

These efforts to experimentally validate violations of the Bell inequalities would later result in Clauser, Aspect, and

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Proceedings of the Conference Foundations of Probability and Physics - 2 : Växjö (Soland), Sweden, June 2-7, 2002

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Harrigan, Nicholas; Spekkens, Robert W. (2010). "Einstein, incompleteness, and the epistemic view of quantum states".

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or "realism", which is not necessarily the same as abandoning realism in a broader philosophical sense. For example,

5925: 3244:{\displaystyle P({\vec {a}},{\vec {b}})=\int d\lambda \,\rho (\lambda )A({\vec {a}},\lambda )B({\vec {b}},\lambda ),} 2434: 17: 13443: 13101: 12101: 7186: 6891:. Physical quantities of interest — position, momentum, energy, spin — are represented by "observables", which are 1601: 11581: 8311:

A similar approach was arrived at independently by Simon Kochen, although never published (private communication).

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Proceedings of the International School of Physics 'Enrico Fermi', Course IL, Foundations of Quantum Mechanics

1461:{\displaystyle |\psi \rangle ={\frac {|0\rangle \otimes |1\rangle -|1\rangle \otimes |0\rangle }{\sqrt {2}}},} 13466: 13288: 13191: 12852: 12664: 12441: 12363: 12235: 12131: 12001: 11939: 8607: 7002:

is its associated eigenvector. More generally, the eigenvalue is degenerate and the probability is given by

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is in fact the largest that quantum physics permits for this combination of expectation values, making it a

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rejected von Neumann's key assumption as early as 1961, but did not publish a criticism of it until 1967.)

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with probability unity. But this is inconsistent with quantum physics: Victor can predict using the state

922: 13673: 13495: 13251: 13111: 12885: 12840: 12784: 12466: 12373: 11934: 9888: 7994: 7952: 6759: 6609: 5785: 2914:), then the outcome of one measurement is certain to be the negative of the outcome of the other, giving 11130:

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

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Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

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See Reichenbach and Jammer, Mermin and Schack, and for Einstein's remarks, Clauser and Shimony and Wick.

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Victor then passes the first qubit to Alice and the second to Bob. Alice and Bob's choices of possible

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Hardy, L. (1993). "Nonlocality for 2 particles without inequalities for almost all entangled states".

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Mermin, N. David (April 1985). "Is the moon there when nobody looks? Reality and the quantum theory".

9771: 7420: 13176: 13141: 13037: 12980: 12526: 12393: 12317: 12278: 12215: 12194: 12151: 12044: 10690: 9479: 8428:; Svetlichny, G. (November 1990). "Nonlocality and Gleason's lemma. Part I. Deterministic theories". 8036:; Tapp, Alain (2005). "Recasting Mermin's multi-player game into the framework of pseudo-telepathy". 6605: 5187: 4202: 3254: 1762:{\displaystyle A_{0}=\sigma _{z},\ A_{1}=\sigma _{x}={\begin{pmatrix}0&1\\1&0\end{pmatrix}};} 9027: 6977: 6870: 6838: 6624:

This is also the route taken by interpretations that descend from the Copenhagen tradition, such as

5646: 4582: 4477: 696:{\displaystyle a_{0}b_{0}+a_{0}b_{1}+a_{1}b_{0}-a_{1}b_{1}=(a_{0}+a_{1})b_{0}+(a_{0}-a_{1})b_{1}\,.} 13349: 13322: 13298: 13261: 13052: 12985: 12920: 12905: 12875: 12798: 12593: 12573: 12563: 12553: 12509: 12069: 11311: 10994: 10917: 9694:"How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival [Excerpt]" 9689: 6749: 6608:

generally take the violation of Bell inequalities as grounds to reject the assumption often called

6287: 5973: 3768:{\displaystyle |P({\vec {a}},{\vec {b}})-P({\vec {a}},{\vec {c}})|\leq 1+P({\vec {b}},{\vec {c}}).} 1269:. Its derivation here depends upon two assumptions: first, that the underlying physical properties 92: 6707:

A few advocates of deterministic models have not given up on local hidden variables. For example,

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measurement upon it. The set of all three particles would then be described by the instruction set

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While only one of these four measurements can be made in a single trial of the experiment, the sum

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provide the responses of the two detectors given the orientation vectors and the hidden variable:

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Bell chose to publish his theorem in a comparatively obscure journal because it did not require

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The BIG Bell Test Collaboration (9 May 2018). "Challenging local realism with human choices".

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are also defined in terms of the Pauli matrices. Alice measures either of the two observables

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Lectures on the Foundations of Physics 1915–1927: Relativity, Quantum Theory and Epistemology

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Victor can calculate the quantum expectation values for pairs of these observables using the

116: 53: 13280: 13029: 12880: 12669: 12598: 12543: 12273: 12081: 12039: 11782: 11727: 11669: 11596: 11546: 11457: 11422: 11380: 11343: 11148: 11081: 11018: 10868: 10709: 10659: 10478: 10433: 10357: 10300: 10235: 10168: 10075: 10018: 9963: 9907: 9844: 9805: 9744: 9655: 9582: 9498: 9397: 9299: 9215: 9168: 9014: 8964: 8839: 8772: 8706: 8572: 8502: 8439: 8338: 8277: 8055: 8003: 7961: 7903: 7750: 7677: 7590: 7541: 7374: 7249: 7227: 6906: 6669:, in which the particles exchange information about their states. This is the basis of the 6649: 6625: 6441: 5855: 5823: 5753: 2289: 1328: 984: 760: 733: 706: 485: 412: 382: 355: 328: 255: 224: 197: 170: 143: 84: 52:, given some basic assumptions about the nature of measurement. "Local" here refers to the 4030:{\displaystyle P({\vec {a}},{\vec {c}})=P({\vec {b}},{\vec {c}})=-{\frac {\sqrt {2}}{2}},} 119:. While the significance of Bell's theorem is not in doubt, its full implications for the 98:

The first rudimentary experiment designed to test Bell's theorem was performed in 1972 by

8: 13599: 13552: 13382: 13156: 12910: 12890: 12825: 12820: 12654: 12623: 12568: 12548: 12456: 12413: 12268: 12179: 12106: 12096: 12008: 10490: 9975: 9698: 9369: 8210: 8184: 6784: 6670: 6177: 4843:

measurement, Victor can predict with probability 1 what result Charlie will return for a

2720: 2570: 1363:

Quantum mechanics can violate the CHSH inequality, as follows. Victor prepares a pair of

11786: 11731: 11673: 11600: 11550: 11461: 11426: 11384: 11347: 11152: 11085: 11030: 11022: 10872: 10713: 10663: 10482: 10437: 10361: 10304: 10239: 10172: 10079: 10022: 9967: 9911: 9848: 9809: 9748: 9659: 9586: 9502: 9303: 9219: 9172: 9018: 8968: 8843: 8776: 8710: 8576: 8506: 8443: 8342: 8290: 8059: 8007: 7965: 7907: 7825: 7754: 7681: 7594: 7545: 7378: 6559: 5727: 5623: 5540: 5497: 5474: 5080: 5057: 4663: 4559: 4454: 4431: 2695: 2672: 462: 439: 305: 282: 60:

can only be influenced by its immediate surroundings, and that interactions mediated by

13315: 13161: 12963: 12900: 12714: 12583: 12481: 12174: 12121: 12013: 11859: 11806: 11772: 11751: 11558: 11497: 11359: 11229: 11193: 11164: 11138: 11105: 11071: 11042: 11008: 10969: 10884: 10858: 10822: 10794: 10752: 10733: 10699: 10649: 10553: 10525: 10524:. The Frontiers Collection. Cham: Springer International Publishing. pp. 175–185. 10502: 10449: 10423: 10348: 10324: 10290: 10256: 10225: 10211: 10192: 10158: 10101: 10042: 10008: 9979: 9953: 9923: 9897: 9868: 9514: 9488: 9422: 9414: 9347: 9231: 9205: 9116: 9108: 9040: 8980: 8954: 8865: 8829: 8796: 8762: 8676: 8660: 8588: 8562: 8544: 8526: 8492: 8463: 8407: 8362: 8302: 8045: 7931: 7839: 7782: 7740: 7711: 7667: 7398: 7364: 7166: 7146: 7126: 7106: 6896: 6764: 6754: 6708: 6446: 6282: 6169: 6158: 6130: 6126:

then some outcome on the second half will be simultaneously impossible and guaranteed.

5520: 4198: 3517: 3468: 2550: 2530: 2506: 2486: 2414: 2394: 2374: 2354: 2334: 2314: 9180: 9036: 8668: 7527: 1352:

exist independently of being observed or measured (sometimes called the assumption of

13579: 13224: 13131: 13088: 13019: 12935: 12915: 12830: 12808: 12724: 12633: 12603: 12531: 12494: 12489: 12471: 12436: 12426: 12230: 12126: 12091: 12074: 11977: 11889: 11879: 11863: 11828: 11798: 11743: 11706: 11696: 11622: 11509: 11501: 11363: 11317: 11221: 11211: 11097: 11046: 11034: 10930: 10826: 10812: 10725: 10638:(1999). "What Do These Correlations Know About Reality? Nonlocality and the Absurd". 10615: 10589: 10579: 10557: 10543: 10506: 10494: 10316: 10261: 10196: 10184: 10093: 10034: 9860: 9671: 9623: 9598: 9594: 9518: 9365: 9288:; Shaknov, I. (1950). "The Angular Correlation of Scattered Annihilation Radiation". 9267: 9257: 9138: 9128: 9088: 9044: 8984: 8920: 8891: 8869: 8857: 8800: 8788: 8753: 8730: 8722: 8697: 8530: 8518: 8467: 8455: 8411: 8399: 8366: 8354: 8294: 8250: 8240: 8188: 8127: 8117: 7859: 7849: 7800: 7774: 7766: 7703: 7693: 7633: 7623: 7602: 7581: 7557: 7508: 7498: 7416: 7390: 7303: 7293: 7285: 6437: 6181: 6138: 6099: 4428:

on her particle, and so do Bob and Charlie. The result of each measurement is either

73: 45: 11842:

Sulcs, S. (2003). "The Nature of Light and Twentieth Century Experimental Physics".

11810: 11755: 11168: 10888: 10737: 10453: 10328: 10046: 9983: 9927: 9235: 8592: 7786: 7402: 6270:{\displaystyle \rho _{AB}=(U\otimes U)\rho _{AB}(U^{\dagger }\otimes U^{\dagger }).} 13246: 13196: 12973: 12451: 12446: 12303: 12184: 11871: 11851: 11794: 11790: 11735: 11677: 11612: 11604: 11554: 11489: 11465: 11430: 11388: 11351: 11233: 11203: 11156: 11109: 11089: 11062: 11026: 10922: 10903: 10876: 10804: 10717: 10685: 10667: 10535: 10486: 10441: 10365: 10312: 10308: 10251: 10247: 10243: 10176: 10149: 10105: 10083: 10030: 10026: 9971: 9915: 9872: 9852: 9835: 9813: 9752: 9663: 9590: 9546: 9506: 9383: 9343: 9339: 9307: 9223: 9176: 9080: 9032: 8972: 8883: 8847: 8780: 8714: 8580: 8510: 8481:

Glick, David; Boge, Florian J. (2019-10-22). "Is the Reality Criterion Analytic?".

8447: 8391: 8346: 8286: 8145: 8109: 8063: 8011: 7969: 7911: 7821: 7762: 7758: 7715: 7685: 7598: 7576: 7549: 7453: 7382: 7355: 6828: 6690: 6645: 6322: 6318: 6054:, each measurement outcome – that is, each vector in the Hilbert space – is either 4284:{\displaystyle |\psi \rangle ={\frac {1}{\sqrt {2}}}(|000\rangle -|111\rangle )\,,} 2716: 9442: 7264:

was one exception, but Jaynes' arguments have not generally been found persuasive.

13372: 13310: 13000: 12995: 12681: 12608: 12588: 12558: 12521: 12516: 12421: 12245: 11818: 11531: 11331: 11197: 10990: 10808: 10786: 10635: 10539: 10411: 9719: 9467: 9393: 9290: 9285: 9156: 9120: 9112: 9084: 8940: 8751:(2007-03-19). "Evidence for the epistemic view of quantum states: A toy theory". 8748: 8664: 8548: 8380:

Stairs, Allen (December 1983). "Quantum Logic, Realism, and Value Definiteness".

8324: 8272: 8268: 8162: 8029: 7989: 7943: 7894: 7877: 7484: 7457: 7425: 6864: 6575: 6526: 6425: 6330: 6278: 6134: 4210: 4206: 1266: 103: 61: 11739: 11160: 10926: 10688:(2010-10-05). "Colloquium : An introduction to consistent quantum theory". 10571: 10445: 9944:

Larsson, Jan-Åke (2014). "Loopholes in Bell inequality tests of local realism".

9818: 9791: 7890:"Can Quantum-Mechanical Description of Physical Reality be Considered Complete?" 6613: 5922:, when they need to have an even number of ones. That is, they win the game iff 91:. Bell then showed that quantum physics predicts correlations that violate this 13481: 13458: 13425: 13229: 13106: 12659: 12628: 12618: 12240: 12220: 12049: 11435: 11410: 10964:

Gill, Richard D. (2002). "Time, Finite Statistics, and Bell's Fifth Position".

10721: 10607: 10414:(2013-01-06). "A Snapshot of Foundational Attitudes Toward Quantum Mechanics". 10125: 9756: 9646:

Bell, J. S. (1966). "On the problem of hidden variables in quantum mechanics".

9568: 8852: 8815: 8784: 8514: 8033: 7881: 7553: 7100: 6728: 6617: 4193: 1525: 65: 12753: 11908: 11855: 11710: 11682: 11655: 11470: 11445: 11207: 10671: 10088: 10061: 9667: 9510: 9388: 9271: 9227: 8976: 8943:; Schack, Rüdiger (2018). "Homer nodded: von Neumann's surprising oversight". 8584: 7637: 7386: 6455:

came close to deriving Bell's theorem in 1960. He considered events where two

6400:

The EPR thought experiment is similar, also considering two separated systems

6129:

This type of argument gained attention when an instance of it was advanced by

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would imply certainty about the outcome of any measurement. Given a value of

5991: 2662: 136: 11893: 9142: 8254: 7863: 7707: 7307: 3458:{\displaystyle A({\vec {a}},\lambda )=\pm 1,\,B({\vec {b}},\lambda )=\pm 1.} 1593:{\displaystyle \sigma _{z}={\begin{pmatrix}1&0\\0&-1\end{pmatrix}}.} 13523: 13448: 12461: 12059: 12054: 11821:; Polak, Wolfgang H. (4 March 2011). "4.4 EPR Paradox and Bell's Theorem". 11802: 11747: 11660: 11406: 11307: 11101: 10880: 10320: 10265: 10188: 10097: 10038: 9864: 9723: 9550: 9471: 9311: 8612: 8176: 7916: 7889: 7885: 7778: 7617: 7488: 7394: 7261: 6832: 6769: 6567: 6530: 6518: 6494: 6173: 6162: 99: 11626: 10370: 10343: 8734: 7660:

Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004

6521:, who then discovered Bell's paper and began to consider how to perform a 6290:, but by construction, the toy model can never violate a Bell inequality. 2715:. The configuration of each measuring instrument is represented by a unit 13533: 13387: 12925: 12499: 11617: 11334:(1981). "Bringing home the atomic world: Quantum mysteries for anybody". 11286: 10974: 10863: 10654: 10066: 9902: 9564: 8767: 8567: 8226: 8050: 7672: 7326: 7245: 7092: 6774: 6469: 6304: 6146: 2524: 2480: 11093: 10180: 6648:

interpretation, is dynamically local, meaning that it does not call for

6482:

to reflect that it would print articles in English, French and Russian.

6329:, and possibly in conversation though not in print by Albert Einstein. ( 79:

The first such result was introduced by Bell in 1964, building upon the

13594: 13528: 13392: 11493: 11265: 9792:"Experimental Test of Bell's Inequalities Using Time-Varying Analyzers" 9535:(1984). "Contextual Hidden Variable Theories and Bell's Inequalities". 9351: 9249: 8912: 8483: 8451: 8350: 8306: 8081: 6820: 6421: 2658: 1368: 11125:"The quantum liar experiment in Cramer's transactional interpretation" 9919: 9675: 8067: 5782:

from Victor, promised to always have an even number of ones, that is,

352:. When Bob receives his particle, he chooses one of two measurements, 13377: 12353: 12034: 11392: 9856: 9619:

John Stewart Bell and Twentieth Century Physics: Vision and Integrity

6900: 6697: 6522: 6508: 4083:{\displaystyle {\frac {\sqrt {2}}{2}}\nleq 1-{\frac {\sqrt {2}}{2}}.} 2863:{\displaystyle P({\vec {a}},{\vec {b}})=-{\vec {a}}\cdot {\vec {b}}.} 2304: 1893: 108: 31: 11946: 11355: 8015: 7974: 7947: 2870:

In particular, if the orientation of the two detectors is the same (

2295: 13562: 13538: 13397: 13362: 11521:

Bell, J. S. (2004). "Bertlmann's Socks and the Nature of Reality".

11411:"Experimental Tests of Realistic Local Theories via Bell's Theorem" 10902:

Jaynes, E. T. (1989). "Clearing up Mysteries — the Original Goal".

10799: 10530: 10295: 10230: 10163: 9493: 8959: 8834: 8497: 8395: 8113: 7369: 4502:, Victor predicts that whenever the three measurements include one 57: 30:"Bell inequality" redirects here. For the related experiments, see 11777: 11143: 11076: 11059: 11013: 10704: 10428: 10013: 9958: 9210: 7745: 6635: 13589: 13206: 11762: 10387:"Nobel physics prize goes to sleuths of 'spooky' quantum science" 10121:"Sorry, Einstein. Quantum Study Suggests 'Spooky Action' Is Real" 9077:

The Infamous Boundary: Seven Decades of Heresy in Quantum Physics

5717:{\displaystyle \sigma _{x}\otimes \sigma _{x}\otimes \sigma _{x}} 4782:{\displaystyle \sigma _{y}\otimes \sigma _{y}\otimes \sigma _{x}} 4729:{\displaystyle \sigma _{y}\otimes \sigma _{x}\otimes \sigma _{y}} 4653:{\displaystyle \sigma _{x}\otimes \sigma _{y}\otimes \sigma _{y}} 41: 10467:

Werner, Reinhard F. (2014-10-24). "Comment on 'What Bell did'".

7930: 7528:"Hidden Variables, Joint Probability, and the Bell Inequalities" 6344:

Consider a mechanical system constituted of two partial systems

13566: 13062: 10385:

Ahlander, Johan; Burger, Ludwig; Pollard, Niklas (2022-10-04).

9832: 8236: 7848:(2nd ed.). Upper Saddle River, NJ: Pearson Prentice Hall. 7352: 7252:, no continuous probability measure on it can be deterministic. 6546:, which would contradict the predictions of quantum mechanics. 6440:

proved that it was indeed deducible from the other postulates.

6142: 2976:. And if the orientations of the two detectors are orthogonal ( 8278:

Proceedings of the Aristotelian Society, Supplementary Volumes

40:

is a term encompassing a number of closely related results in

12835: 11915: 9996: 7099:

either 0 or 1. For example, a Stern–Gerlach measurement on a

6629: 5620:

and the product of Alice, Bob, and Charlie's results will be

3567:

of settings for the second detector: it can be set either to

1364: 11582:"Proposal for a loophole-free test of the Bell inequalities" 11202:. Fundamental Theories of Physics. Vol. 185. Springer. 4209:

presented a four-particle thought experiment in 1990, which

13584: 13057: 12990: 10791:

Quantum Nonlocality and Reality: 50 years of Bell's theorem

10409: 9256:(Dover reprint ed.). Prentice-Hall. pp. 614–623. 7663: 6456: 1103:{\displaystyle a_{0}b_{0}+a_{0}b_{1}+a_{1}b_{0}-a_{1}b_{1}} 11199:

The Cellular Automaton Interpretation of Quantum Mechanics

8327:(May 1983). "Nonlocality and the Kochen–Specker paradox". 7658:(2004). "Consequences and limits of nonlocal strategies". 6628:(often advertised as "Copenhagen done right"), as well as 6368:

of the determining magnitudes specifying the condition of

1110:

across all the trials will be less than or equal to 2. No

13201: 13186: 11909:

Mermin: Spooky Actions At A Distance? Oppenheimer Lecture

11649:. Berlin-Heidelberg-New York: Springer. pp. 103–117. 10968:. Vol. 5. Växjö University Press. pp. 179–206. 10847:(2000). "Information flow in entangled quantum systems". 10753:"Quantum-Bayesian and Pragmatist Views of Quantum Theory" 6549:

The most prevalent loopholes in real experiments are the

3862:

lie in their plane at a 45° angle from both of them. Then

2637:{\displaystyle {\frac {2+{\sqrt {2}}}{4}}\approx 0.85\,.} 11512:(1971). "Introduction to the hidden variable question". 11300:

The Age of Entanglement: When Quantum Physics Was Reborn

10344:"Closing the Door on Einstein and Bohr's Quantum Debate" 7619:

Quantum theory : an information processing approach

7579:(August 1990). "Wringing out better Bell inequalities". 6413:

implies the existence of an "element of reality" within

5184:

measurement, then the product of their results would be

5047:{\displaystyle (a_{x},a_{y},b_{x},b_{y},c_{x},c_{y})\,,} 7728: 7497:(2nd ed.). Cambridge: Cambridge University Press. 6835:, the state of a quantum mechanical system is a vector 7650: 6711:

has argued that superdeterminism cannot be dismissed.

2309:

in which Alice and Bob try to coordinate their actions

1725: 1553: 10384: 9790:

Aspect, Alain; Dalibard, Jean; Roger, Gérard (1982).

9728:"Experimental test of local hidden-variable theories" 9370:"Measures on the closed subspaces of a Hilbert space" 9000:"Bell's theorem: Experimental tests and implications" 8028: 7876: 7230: 7189: 7169: 7149: 7129: 7109: 7052: 7008: 6980: 6929: 6909: 6873: 6841: 6190: 6141:. The Conway–Kochen theorem uses a pair of entangled 6111: 6076: 6040: 6020: 6000: 5928: 5890: 5858: 5826: 5788: 5756: 5730: 5677: 5649: 5626: 5566: 5543: 5523: 5500: 5477: 5237: 5190: 5163: 5133: 5106: 5083: 5060: 4958: 4931: 4904: 4876: 4849: 4822: 4795: 4742: 4689: 4666: 4613: 4585: 4562: 4535: 4508: 4480: 4457: 4434: 4407: 4380: 4353: 4325: 4297: 4219: 4154: 4125: 4096: 4043: 3930: 3868: 3839: 3810: 3781: 3631: 3602: 3573: 3540: 3520: 3491: 3471: 3378: 3334: 3290: 3257: 3122: 3102: 3032: 2982: 2920: 2876: 2787: 2758: 2729: 2698: 2675: 2601: 2573: 2553: 2533: 2509: 2489: 2437: 2417: 2397: 2391:

to Bob. Alice and Bob win if they return answer bits

2377: 2357: 2337: 2317: 2267: 2111: 1902: 1775: 1664: 1637: 1610: 1534: 1502: 1474: 1376: 1331: 1275: 1121: 1010: 987: 925: 869: 826: 786: 763: 736: 709: 515: 488: 465: 442: 415: 385: 358: 331: 308: 285: 258: 227: 200: 173: 146: 9472:"Hidden Variables and the Two Theorems of John Bell" 9462: 9460: 9458: 9125:

Quantum speakables: From Bell to Quantum Information

9115:(2002). "The Geometry of the Quantum Paradoxes". In 7248:

of the Hilbert space, and since this unit sphere is

7039:{\displaystyle \langle \psi |P_{\eta }\psi \rangle } 6718: 5154:

measurement simply returning the appropriate value.

459:, then the particle she received carried a value of 13028: 9789: 9773:

Experimental test of local hidden-variable theories

7095:implies that the probability of a given outcome is 106:. More advanced experiments, known collectively as 11260:The following are intended for general audiences. 10470:Journal of Physics A: Mathematical and Theoretical 9946:Journal of Physics A: Mathematical and Theoretical 8275:(1991-07-01). "Nonlocality in Quantum Mechanics". 7236: 7216: 7175: 7155: 7135: 7115: 7065: 7038: 6994: 6966: 6923:is non-degenerate and the probability is given by 6915: 6883: 6855: 6269: 6117: 6082: 6046: 6026: 6006: 5964: 5914: 5876: 5844: 5812: 5774: 5739: 5716: 5663: 5635: 5612: 5552: 5529: 5509: 5486: 5463: 5223: 5176: 5146: 5119: 5092: 5069: 5046: 4944: 4917: 4889: 4862: 4835: 4808: 4781: 4728: 4675: 4652: 4599: 4571: 4548: 4521: 4494: 4474:. Applying the Born rule to the three-qubit state 4466: 4443: 4420: 4393: 4366: 4339: 4311: 4283: 4172: 4140: 4111: 4082: 4029: 3916: 3854: 3825: 3796: 3767: 3617: 3588: 3555: 3526: 3506: 3477: 3457: 3364: 3320: 3272: 3243: 3108: 3085:. Bell proves by example that these special cases 3077: 3018: 2968: 2906: 2862: 2773: 2744: 2707: 2684: 2636: 2587: 2559: 2539: 2515: 2495: 2471: 2423: 2403: 2383: 2363: 2343: 2323: 2280: 2252: 2097: 1884: 1761: 1650: 1623: 1592: 1516: 1488: 1460: 1344: 1317: 1257: 1102: 996: 973: 911: 855: 812: 772: 749: 722: 695: 501: 474: 451: 428: 398: 371: 344: 317: 294: 271: 240: 213: 186: 159: 83:, which had called attention to the phenomenon of 10761:. Metaphysics Research Lab, Stanford University. 9885: 9569:"Two simple proofs of the Kochen-Specker theorem" 9455: 6967:{\displaystyle |\langle \eta |\psi \rangle |^{2}} 6145:and a Kochen–Specker configuration discovered by 5884:have an odd number of ones for all inputs except 2646: 13640: 10895: 9451:. Metaphysics Research Lab, Stanford University. 9193: 6600: 5979: 2719:, and the quantum-mechanical prediction for the 12783: 11525:. Cambridge University Press. pp. 139–158. 10793:. Cambridge University Press. pp. 91–123. 10781: 10779: 10062:"Quantum 'spookiness' passes toughest test yet" 9718: 9328:(1957). "Quantum Mechanics and Hilbert Space". 8424: 7574: 6636:Many-worlds interpretation of quantum mechanics 6558:opened when the detections are not done with a 5965:{\displaystyle a\oplus b\oplus c=x\lor y\lor z} 4556:'s, the product of the outcomes will always be 11529: 11523:Speakable and Unspeakable in Quantum Mechanics 11478: 10614:. Princeton University Press. pp. 26–29. 10210:Shalm, L. K.; et al. (16 December 2015). 9574:Journal of Physics A: Mathematical and General 8997: 8890:. University of California Press. p. 14. 8814:Catani, Lorenzo; Browne, Dan E. (2017-07-27). 8635:"John Conway – discovering free will (part I)" 8322: 7479: 7477: 7475: 7473: 7290:Speakable and Unspeakable in Quantum Mechanics 6152: 6066:when considered as belonging to one basis and 2303:The CHSH inequality can also be thought of as 1769:and Bob measures either of the two observables 12769: 11962: 11400:The following are more technically oriented. 11276: 11270:Entanglement: The greatest mystery in physics 10839: 10272: 10203: 9538:British Journal for the Philosophy of Science 8907: 8905: 8158:Mathematical Foundations of Quantum Mechanics 8104:(2009). Sauer, Tilman; Majer, Ulrich (eds.). 8022: 7483: 7217:{\displaystyle u\to \langle \rho u,u\rangle } 6659: 6090:can be controlling the measurement outcomes. 1265:This is a Bell inequality, specifically, the 11870: 11817: 11579: 11192: 10988: 10785: 10776: 10410:Schlosshauer, Maximilian; Kofler, Johannes; 10212:"Strong Loophole-Free Test of Local Realism" 10140: 10112: 9939: 9937: 9404: 9107: 8939: 8888:Philosophic Foundations of Quantum Mechanics 8813: 8659: 8543: 8267: 8150:Mathematische Grundlagen der Quantenmechanik 7211: 7196: 7033: 7009: 6989: 6949: 6935: 6850: 6476:, the covers carried the trilingual version 6372:has been measured (for instance coordinates 5658: 4594: 4489: 4334: 4306: 4271: 4257: 4228: 3019:{\displaystyle {\vec {a}}\cdot {\vec {b}}=0} 2351:, independently and at random. He sends bit 2234: 2208: 2202: 2176: 2170: 2144: 2138: 2112: 2070: 2044: 2023: 1997: 1976: 1950: 1929: 1903: 1511: 1483: 1444: 1430: 1416: 1402: 1385: 1237: 1214: 1208: 1185: 1179: 1156: 1150: 1127: 9641: 9639: 9358: 8882: 8144: 7494:Quantum Computation and Quantum Information 7470: 7346: 5990:In quantum theory, orthonormal bases for a 5157:If Alice, Bob, and Charlie all perform the 3917:{\displaystyle P({\vec {a}},{\vec {b}})=0,} 3026:), then the outcomes are uncorrelated, and 2969:{\displaystyle P({\vec {a}},{\vec {a}})=-1} 2479:Or, equivalently, Alice and Bob win if the 12776: 12762: 11969: 11955: 11644: 10146: 9779:(PhD). University of California, Berkeley. 8902: 8181:The Theory of Groups and Quantum Mechanics 7982: 7444: 7442: 7292:. Cambridge University Press. p. 65. 4789:. Therefore, knowing Alice's result for a 3078:{\displaystyle P({\vec {a}},{\vec {b}})=0} 11776: 11690: 11681: 11653: 11616: 11469: 11434: 11142: 11075: 11012: 10973: 10916: 10862: 10798: 10703: 10684: 10653: 10529: 10427: 10369: 10294: 10255: 10229: 10162: 10087: 10012: 9957: 9934: 9901: 9817: 9492: 9434: 9387: 9284: 9209: 9026: 8958: 8851: 8833: 8766: 8566: 8496: 8480: 8049: 7973: 7915: 7838: 7744: 7671: 7415: 7368: 5606: 5457: 5040: 4347:are the eigenvectors of the Pauli matrix 4277: 3418: 3171: 2630: 2465: 2461: 2460: 2091: 1251: 689: 11824:Quantum Computing: A Gentle Introduction 11654:Goldstein, Sheldon; et al. (2011). 11580:Fry, E. S.; Walther, T.; Li, S. (1995). 11279:The Einstein, Podolsky and Rosen Paradox 10957: 10519: 10278: 9769: 9636: 9615: 9155: 8747: 8608:"Do subatomic particles have free will?" 8605: 7805:"On the Einstein Podolsky Rosen Paradox" 7793: 7421:"Experiment Reaffirms Quantum Weirdness" 6493: 2294: 919:must equal 0, while in the latter case, 13294:Continuous-variable quantum information 11285: 11122: 10606: 10576:The Interpretation of Quantum Mechanics 10118: 9943: 9826: 9531: 9364: 9079:. New York: Springer. pp. 92–100. 8100: 7992:(1990). "Quantum mysteries revisited". 7924: 7439: 14: 13641: 11443: 11405: 11370: 11330: 11306: 11297: 10901: 10750: 10634: 10466: 10341: 10059: 9688: 9466: 9443:"Quantum Logic and Probability Theory" 9375:Indiana University Mathematics Journal 9324: 9127:. Berlin: Springer. pp. 257–269. 9075:Wick, David (1995). "Bell's Theorem". 8911: 8694: 8632: 8379: 7988: 6903:: in the simplest case the eigenvalue 6463: 3365:{\displaystyle B({\vec {b}},\lambda )} 3321:{\displaystyle A({\vec {a}},\lambda )} 12757: 11976: 11950: 11876:Quantum Mechanics: An Empiricist View 11841: 11717: 11272:. New York: Four Walls Eight Windows. 11264: 10570: 10564: 10209: 9563: 9440: 9159:(March 1936). "Physics and reality". 9070: 9068: 8225: 8080: 7948:"Bell's theorem without inequalities" 7332:The Royal Swedish Academy of Sciences 6431:By the late 1940s, the mathematician 6014:exists, so that knowing the value of 5613:{\displaystyle a_{x}b_{x}c_{x}=+1\,,} 2907:{\displaystyle {\vec {a}}={\vec {b}}} 11520: 11508: 11281:. New York and London: Plenum Press. 10963: 10905:Maximum Entropy and Bayesian Methods 9645: 9415:"Andy Gleason and Quantum Mechanics" 9410: 9248: 9074: 8998:Clauser, J. F.; Shimony, A. (1978). 8232:Quantum Theory: Concepts and Methods 8175: 7799: 7525: 7284: 7244:. This mapping is continuous on the 6790:Renninger negative-result experiment 6592:Interpretations of quantum mechanics 6093: 5537:. Each factor in parentheses equals 4187: 2723:between two detectors with settings 974:{\displaystyle (a_{0}+a_{1})b_{0}=0} 11921:Internet Encyclopedia of Philosophy 10758:Stanford Encyclopedia of Philosophy 10342:Aspect, Alain (December 16, 2015). 9770:Freedman, Stuart Jay (1972-05-05). 9448:Stanford Encyclopedia of Philosophy 8917:The Philosophy of Quantum Mechanics 8087:The Principles of Quantum Mechanics 8038:Quantum Information and Computation 7870: 7826:10.1103/PhysicsPhysiqueFizika.1.195 7615: 7463:Stanford Encyclopedia of Philosophy 7448: 6684: 6499:Scheme of a "two-channel" Bell test 5813:{\displaystyle x\oplus y\oplus z=0} 4816:measurement and Bob's result for a 3465:Crucially, the outcome of detector 863:. In the former case, the quantity 121:interpretation of quantum mechanics 24: 11559:10.1038/scientificamerican1179-158 11255: 10850:Proceedings of the Royal Society A 9609: 9065: 8202:Gruppentheorie und Quantenmechanik 6876: 6585: 6376:momenta). Since there can be only 6315:1932 textbook on quantum mechanics 1524:are the eigenstates of one of the 1318:{\displaystyle a_{0},a_{1},b_{0},} 912:{\displaystyle (a_{0}-a_{1})b_{1}} 25: 13690: 11902: 10522:Quantum [Un]Speakables II 10119:Markoff, Jack (21 October 2015). 9331:The American Mathematical Monthly 9161:Journal of the Franklin Institute 8551:(2006). "The Free Will Theorem". 8291:10.1093/aristoteliansupp/65.1.119 8165:Princeton University Press. 1955. 7845:Introduction to Quantum Mechanics 7322:"The Nobel Prize in Physics 2022" 7091:A hidden-variable theory that is 64:cannot propagate faster than the 13623: 13622: 13613: 13612: 12738: 12737: 11532:"The Quantum Theory and Reality" 11444:Aspect, A.; et al. (1982). 11277:Afriat, A.; Selleri, F. (1999). 10612:Surprises in Theoretical Physics 10060:Merali, Zeeya (27 August 2015). 6819:In more detail, as developed by 6721: 6533:and collaborators performed the 5231:. This value can be deduced from 11633:from the original on 2021-12-29 11568:from the original on 2009-03-27 11240:from the original on 2021-12-29 11186: 11175:from the original on 2018-06-24 11116: 11053: 10982: 10946:from the original on 2011-10-28 10833: 10765:from the original on 2021-08-17 10744: 10678: 10628: 10600: 10513: 10460: 10403: 10378: 10335: 10053: 9990: 9879: 9783: 9763: 9712: 9682: 9557: 9525: 9318: 9278: 9242: 9187: 9149: 9101: 9054:from the original on 2017-09-23 8991: 8933: 8876: 8807: 8741: 8688: 8653: 8626: 8599: 8537: 8474: 8418: 8373: 8316: 8261: 8219: 8169: 8138: 8094: 8074: 7832: 7722: 7644: 7609: 7255: 7085: 7076: 6813: 6606:Copenhagen-type interpretations 6525:in the laboratory. Clauser and 6172:introduced what are now called 5224:{\displaystyle a_{x}b_{x}c_{x}} 3273:{\displaystyle \rho (\lambda )} 2472:{\displaystyle xy=a+b\mod 2\,.} 2456: 81:Einstein–Podolsky–Rosen paradox 12687:Relativistic quantum mechanics 11795:10.1103/physrevlett.100.150404 11695:. Cambridge University Press. 10578:. Princeton University Press. 10491:10.1088/1751-8113/47/42/424011 10313:10.1103/PhysRevLett.115.250401 10248:10.1103/PhysRevLett.115.250402 10031:10.1103/PhysRevLett.107.170404 9976:10.1088/1751-8113/47/42/424003 9344:10.1080/00029890.1957.11989120 9007:Reports on Progress in Physics 8669:"The strong free will theorem" 8606:Rehmeyer, Julie (2008-08-15). 7763:10.1103/PhysRevLett.104.140401 7568: 7519: 7409: 7314: 7278: 7193: 7016: 6995:{\displaystyle |\eta \rangle } 6982: 6954: 6942: 6931: 6884:{\displaystyle {\mathcal {H}}} 6856:{\displaystyle |\psi \rangle } 6843: 6803: 6738:Einstein's thought experiments 6489: 6317:, the Hungarian-born polymath 6261: 6235: 6219: 6207: 5664:{\displaystyle |\psi \rangle } 5651: 5343: 5310: 5307: 5274: 5271: 5238: 5037: 4959: 4600:{\displaystyle |\psi \rangle } 4587: 4495:{\displaystyle |\psi \rangle } 4482: 4327: 4299: 4274: 4264: 4250: 4246: 4221: 4161: 4132: 4103: 4003: 3997: 3982: 3973: 3964: 3958: 3943: 3934: 3902: 3896: 3881: 3872: 3846: 3817: 3788: 3759: 3753: 3738: 3729: 3713: 3709: 3703: 3688: 3679: 3670: 3664: 3649: 3640: 3633: 3609: 3580: 3547: 3514:, and likewise the outcome of 3498: 3443: 3431: 3422: 3403: 3391: 3382: 3359: 3347: 3338: 3315: 3303: 3294: 3267: 3261: 3235: 3223: 3214: 3208: 3196: 3187: 3181: 3175: 3156: 3150: 3135: 3126: 3066: 3060: 3045: 3036: 3004: 2989: 2954: 2948: 2933: 2924: 2898: 2883: 2851: 2836: 2821: 2815: 2800: 2791: 2765: 2736: 2651: 2647:Variations and related results 1504: 1476: 1437: 1423: 1409: 1395: 1378: 1241: 1123: 952: 926: 896: 870: 676: 650: 634: 608: 406:, which are also both binary. 50:local hidden-variable theories 44:, all of which determine that 13: 1: 13659:Theorems in quantum mechanics 13289:Adiabatic quantum computation 12665:Quantum statistical mechanics 12442:Quantum differential calculus 12364:Delayed-choice quantum eraser 12132:Symmetry in quantum mechanics 11827:. MIT Press. pp. 60–65. 11291:The Meaning of Quantum Theory 11123:Kastner, Ruth E. (May 2010). 11031:10.1088/1367-2630/17/3/033002 10755:. In Zalta, Edward N. (ed.). 9181:10.1016/S0016-0032(36)91047-5 8633:Thomas, Rachel (2011-12-27). 7271: 6601:The Copenhagen interpretation 6298: 5980:Kochen–Specker theorem (1967) 5471:because the square of either 5054:with each entry being either 13340:Topological quantum computer 11302:. New York: Alfred A. Knopf. 10809:10.1017/CBO9781316219393.008 10540:10.1007/978-3-319-38987-5_10 9085:10.1007/978-1-4612-4030-3_11 7603:10.1016/0003-4916(90)90339-P 6679:transactional interpretation 6544:local hidden-variable theory 6309:History of quantum mechanics 3282:probability density function 2311:. Victor prepares two bits, 2281:{\displaystyle 2{\sqrt {2}}} 856:{\displaystyle a_{0}=-a_{1}} 252:measurements: the result of 7: 13649:Quantum information science 13618:Quantum information science 12785:Quantum information science 12467:Quantum stochastic calculus 12457:Quantum measurement problem 12379:Mach–Zehnder interferometer 11935:Encyclopedia of Mathematics 11740:10.1103/physrevlett.71.1665 11336:American Journal of Physics 11161:10.1016/j.shpsb.2010.01.001 10927:10.1007/978-94-015-7860-8_1 10446:10.1016/j.shpsb.2013.04.004 9889:American Journal of Physics 9819:10.1103/PhysRevLett.49.1804 9622:. Oxford University Press. 9037:10.1088/0034-4885/41/12/002 8199:Translated from the German 7995:American Journal of Physics 7953:American Journal of Physics 7622:. Oxford University Press. 7526:Fine, Arthur (1982-02-01). 6714: 6610:counterfactual definiteness 6513:In 1967, the unusual title 6153:Quasiclassical entanglement 5177:{\displaystyle \sigma _{x}} 5147:{\displaystyle \sigma _{y}} 5120:{\displaystyle \sigma _{x}} 4945:{\displaystyle \sigma _{y}} 4918:{\displaystyle \sigma _{x}} 4890:{\displaystyle \sigma _{y}} 4863:{\displaystyle \sigma _{y}} 4836:{\displaystyle \sigma _{y}} 4809:{\displaystyle \sigma _{x}} 4549:{\displaystyle \sigma _{y}} 4522:{\displaystyle \sigma _{x}} 4421:{\displaystyle \sigma _{y}} 4394:{\displaystyle \sigma _{x}} 4367:{\displaystyle \sigma _{z}} 4173:{\displaystyle {\vec {c}}.} 1651:{\displaystyle \sigma _{x}} 1624:{\displaystyle \sigma _{z}} 813:{\displaystyle a_{0}=a_{1}} 10: 13695: 13013:quantum gate teleportation 11436:10.1103/physrevlett.47.460 11293:. Oxford University Press. 10722:10.1103/RevModPhys.82.2835 9757:10.1103/PhysRevLett.28.938 9595:10.1088/0305-4470/24/4/003 8785:10.1103/PhysRevA.75.032110 8515:10.1007/s10670-019-00163-w 8090:. Oxford: Clarendon Press. 8082:Dirac, Paul Adrien Maurice 7554:10.1103/PhysRevLett.48.291 7224:for some density operator 6688: 6660:Non-local hidden variables 6642:Many-worlds interpretation 6589: 6506: 6302: 6293: 6156: 6097: 5983: 4340:{\displaystyle |1\rangle } 4312:{\displaystyle |0\rangle } 4191: 4141:{\displaystyle {\vec {b}}} 4112:{\displaystyle {\vec {a}}} 3855:{\displaystyle {\vec {c}}} 3826:{\displaystyle {\vec {b}}} 3797:{\displaystyle {\vec {a}}} 3618:{\displaystyle {\vec {c}}} 3589:{\displaystyle {\vec {b}}} 3556:{\displaystyle {\vec {a}}} 3507:{\displaystyle {\vec {b}}} 2774:{\displaystyle {\vec {b}}} 2745:{\displaystyle {\vec {a}}} 1517:{\displaystyle |1\rangle } 1489:{\displaystyle |0\rangle } 1367:which he describes by the 509:. Consider the combination 126: 29: 13608: 13551: 13514: 13480: 13457: 13424: 13415: 13348: 13277: 13215: 13175: 13142:Quantum Fourier transform 13087: 13038:Post-quantum cryptography 12981:Entanglement distillation 12954: 12863: 12791: 12733: 12695: 12647: 12527:Quantum complexity theory 12505:Quantum cellular automata 12480: 12412: 12346: 12259: 12208: 12195:Path integral formulation 12162: 12027: 11984: 11693:Consistent Quantum Theory 11691:Griffiths, R. B. (2001). 11683:10.4249/scholarpedia.8378 11471:10.1103/physrevlett.49.91 11208:10.1007/978-3-319-41285-6 10691:Reviews of Modern Physics 10089:10.1038/nature.2015.18255 9668:10.1103/revmodphys.38.447 9648:Reviews of Modern Physics 9616:Whitaker, Andrew (2016). 9511:10.1103/RevModPhys.65.803 9480:Reviews of Modern Physics 9389:10.1512/iumj.1957.6.56050 9228:10.1007/s10701-009-9347-0 8977:10.1007/s10701-018-0197-5 8585:10.1007/s10701-006-9068-6 7387:10.1038/s41586-018-0085-3 7066:{\displaystyle P_{\eta }} 5820:, and send him back bits 13628:Quantum mechanics topics 13323:Quantum machine learning 13299:One-way quantum computer 13152:Quantum phase estimation 13053:Quantum key distribution 12986:Monogamy of entanglement 12594:Quantum machine learning 12574:Quantum key distribution 12564:Quantum image processing 12554:Quantum error correction 12404:Wheeler's delayed choice 11609:10.1103/physreva.52.4381 11482:Lettere al Nuovo Cimento 11313:The Fabric of the Cosmos 10751:Healey, Richard (2016). 8853:10.1088/1367-2630/aa781c 8719:10.1103/PhysRevA.40.4277 7690:10.1109/CCC.2004.1313847 7654:; Hoyer, P.; Toner, B.; 6796: 6750:Fundamental Fysiks Group 6517:caught the attention of 6118:{\displaystyle \lambda } 6083:{\displaystyle \lambda } 6047:{\displaystyle \lambda } 6027:{\displaystyle \lambda } 6007:{\displaystyle \lambda } 5974:quantum pseudo-telepathy 5747:with probability unity. 3109:{\displaystyle \lambda } 135:Hypothetical characters 13235:Randomized benchmarking 13097:Amplitude amplification 12510:Quantum finite automata 11856:10.1023/A:1026323203487 11720:Physical Review Letters 11530:D'Espagnat, B. (1979). 11298:Gilder, Louisa (2008). 10672:10.1023/A:1018864225930 10282:Physical Review Letters 10217:Physical Review Letters 10000:Physical Review Letters 9797:Physical Review Letters 9736:Physical Review Letters 8919:. John Wiley and Sons. 7813:Physics Physique Физика 7732:Physical Review Letters 7575:Braunstein, Samuel L.; 7533:Physical Review Letters 6760:Leggett–Garg inequality 6744:Epistemological Letters 6578:being awarded the 2022 6515:Physics Physique Физика 6479:Physics Physique Физика 5915:{\displaystyle x=y=z=0} 5852:. They win the game if 4579:. This follows because 3833:be orthogonal, and let 436:and obtains the result 13664:Hidden variable theory 13335:Quantum Turing machine 13328:quantum neural network 13075:Quantum secret sharing 12614:Quantum neural network 11844:Foundations of Science 11409:; et al. (1981). 11000:New Journal of Physics 10989:Wood, Christopher J.; 10881:10.1098/rspa.2000.0585 10641:Foundations of Physics 9312:10.1103/PhysRev.77.136 9197:Foundations of Physics 9117:Bertlmann, Reinhold A. 8946:Foundations of Physics 8821:New Journal of Physics 8554:Foundations of Physics 8431:Foundations of Physics 8330:Foundations of Physics 8325:Redhead, Michael L. G. 7917:10.1103/PhysRev.47.777 7238: 7218: 7177: 7157: 7137: 7117: 7067: 7040: 6996: 6968: 6917: 6885: 6857: 6667:hidden variable theory 6580:Nobel Prize in Physics 6504: 6380:physical condition of 6271: 6137:under the name of the 6119: 6084: 6048: 6028: 6008: 5986:Kochen–Specker theorem 5966: 5916: 5878: 5846: 5814: 5776: 5741: 5718: 5665: 5637: 5614: 5554: 5531: 5511: 5488: 5465: 5225: 5178: 5148: 5121: 5094: 5071: 5048: 4946: 4919: 4891: 4864: 4837: 4810: 4783: 4730: 4677: 4654: 4601: 4573: 4550: 4523: 4496: 4468: 4445: 4422: 4395: 4368: 4341: 4313: 4285: 4174: 4142: 4113: 4084: 4031: 3918: 3856: 3827: 3798: 3769: 3619: 3590: 3557: 3528: 3508: 3479: 3459: 3366: 3322: 3274: 3245: 3110: 3079: 3020: 2970: 2908: 2864: 2775: 2746: 2709: 2686: 2638: 2589: 2561: 2541: 2517: 2497: 2473: 2431:to Victor, satisfying 2425: 2405: 2385: 2365: 2345: 2325: 2300: 2282: 2254: 2099: 1886: 1763: 1652: 1625: 1594: 1518: 1490: 1462: 1346: 1319: 1259: 1104: 998: 975: 913: 857: 814: 774: 751: 724: 697: 503: 476: 453: 430: 400: 373: 346: 319: 296: 273: 242: 215: 188: 161: 13407:Entanglement-assisted 13368:quantum convolutional 13043:Quantum coin flipping 13008:Quantum teleportation 12969:entanglement-assisted 12799:DiVincenzo's criteria 12639:Quantum teleportation 12152:Wave–particle duality 10371:10.1103/Physics.8.123 8383:Philosophy of Science 8154:English translation: 7239: 7237:{\displaystyle \rho } 7219: 7178: 7158: 7138: 7118: 7068: 7041: 6997: 6969: 6918: 6916:{\displaystyle \eta } 6886: 6858: 6780:Quantum contextuality 6497: 6272: 6120: 6085: 6049: 6029: 6009: 5967: 5917: 5879: 5877:{\displaystyle a,b,c} 5847: 5845:{\displaystyle a,b,c} 5815: 5777: 5775:{\displaystyle x,y,z} 5742: 5719: 5671:that the measurement 5666: 5638: 5615: 5555: 5532: 5512: 5489: 5466: 5226: 5179: 5149: 5122: 5095: 5072: 5049: 4947: 4920: 4892: 4865: 4838: 4811: 4784: 4731: 4678: 4655: 4607:is an eigenvector of 4602: 4574: 4551: 4524: 4497: 4469: 4446: 4423: 4396: 4369: 4342: 4314: 4286: 4175: 4143: 4114: 4085: 4032: 3919: 3857: 3828: 3799: 3770: 3620: 3591: 3558: 3534:does not depend upon 3529: 3509: 3485:does not depend upon 3480: 3460: 3367: 3323: 3275: 3246: 3111: 3080: 3021: 2971: 2909: 2865: 2776: 2747: 2710: 2687: 2639: 2590: 2562: 2542: 2518: 2498: 2474: 2426: 2406: 2386: 2366: 2346: 2326: 2298: 2283: 2255: 2100: 1887: 1764: 1653: 1626: 1595: 1519: 1491: 1463: 1347: 1345:{\displaystyle b_{1}} 1320: 1260: 1105: 999: 997:{\displaystyle \pm 2} 976: 914: 858: 815: 775: 773:{\displaystyle \pm 1} 752: 750:{\displaystyle a_{1}} 725: 723:{\displaystyle a_{0}} 698: 504: 502:{\displaystyle a_{0}} 477: 454: 431: 429:{\displaystyle A_{0}} 401: 399:{\displaystyle B_{1}} 374: 372:{\displaystyle B_{0}} 347: 345:{\displaystyle A_{1}} 320: 297: 274: 272:{\displaystyle A_{0}} 243: 241:{\displaystyle A_{1}} 216: 214:{\displaystyle A_{0}} 189: 187:{\displaystyle A_{1}} 162: 160:{\displaystyle A_{0}} 54:principle of locality 48:is incompatible with 13218:processor benchmarks 13147:Quantum optimization 13030:Quantum cryptography 12841:physical vs. logical 12670:Quantum field theory 12599:Quantum metamaterial 12544:Quantum cryptography 12274:Consistent histories 9551:10.1093/bjps/35.1.25 7666:. pp. 236–249. 7616:Rau, Jochen (2021). 7228: 7187: 7167: 7147: 7127: 7107: 7050: 7006: 6978: 6927: 6907: 6871: 6839: 6650:action at a distance 6644:, also known as the 6626:consistent histories 6560:spacelike separation 6503:coincidence monitor. 6354:Schrödinger equation 6325:, in more detail by 6188: 6109: 6074: 6038: 6018: 5998: 5926: 5888: 5856: 5824: 5786: 5754: 5728: 5675: 5647: 5624: 5564: 5541: 5521: 5498: 5475: 5235: 5188: 5161: 5131: 5104: 5081: 5058: 4956: 4929: 4902: 4874: 4847: 4820: 4793: 4740: 4687: 4664: 4611: 4583: 4560: 4533: 4506: 4478: 4455: 4432: 4405: 4378: 4351: 4323: 4295: 4217: 4152: 4123: 4094: 4041: 3928: 3866: 3837: 3808: 3779: 3629: 3600: 3571: 3538: 3518: 3489: 3469: 3376: 3332: 3288: 3284:. The two functions 3255: 3120: 3100: 3030: 2980: 2918: 2874: 2785: 2756: 2727: 2696: 2673: 2667:Stern–Gerlach device 2599: 2571: 2551: 2531: 2507: 2487: 2435: 2415: 2395: 2375: 2355: 2335: 2315: 2265: 2109: 1900: 1773: 1662: 1635: 1608: 1532: 1500: 1472: 1374: 1329: 1273: 1119: 1008: 985: 923: 867: 824: 784: 761: 734: 707: 513: 486: 463: 440: 413: 383: 356: 329: 306: 283: 256: 225: 198: 171: 144: 85:quantum entanglement 13654:Quantum measurement 12931:Quantum speed limit 12826:Quantum programming 12821:Quantum information 12655:Quantum fluctuation 12624:Quantum programming 12584:Quantum logic gates 12569:Quantum information 12549:Quantum electronics 12009:Classical mechanics 11930:"Bell inequalities" 11878:. Clarendon Press. 11872:van Fraassen, B. C. 11819:Rieffel, Eleanor G. 11787:2008PhRvL.100o0404M 11732:1993PhRvL..71.1665H 11674:2011SchpJ...6.8378G 11601:1995PhRvA..52.4381F 11551:1979SciAm.241e.158D 11539:Scientific American 11462:1982PhRvL..49...91A 11427:1981PhRvL..47..460A 11385:1985PhT....38d..38M 11348:1981AmJPh..49..940M 11153:2010SHPMP..41...86K 11094:10.1038/nature05677 11086:2007Natur.446..871G 11023:2015NJPh...17c3002W 10991:Spekkens, Robert W. 10873:2000RSPSA.456.1759D 10857:(1999): 1759–1774. 10714:2010RvMP...82.2835H 10664:1998quant.ph..7055M 10483:2014JPhA...47P4011W 10438:2013SHPMP..44..222S 10362:2015PhyOJ...8..123A 10305:2015PhRvL.115y0401G 10240:2015PhRvL.115y0402S 10181:10.1038/nature15759 10173:2015Natur.526..682H 10080:2015Natur.525...14M 10023:2011PhRvL.107q0404G 9968:2014JPhA...47P4003L 9912:2002AmJPh..70..903D 9849:2000Natur.403..515P 9810:1982PhRvL..49.1804A 9749:1972PhRvL..28..938F 9699:Scientific American 9660:1966RvMP...38..447B 9587:1991JPhA...24L.175P 9503:1993RvMP...65..803M 9304:1950PhRv...77..136W 9220:2010FoPh...40..125H 9173:1936FrInJ.221..349E 9019:1978RPPh...41.1881C 8969:2018FoPh...48.1007M 8844:2017NJPh...19g3035C 8777:2007PhRvA..75c2110S 8749:Spekkens, Robert W. 8711:1989PhRvA..40.4277W 8577:2006FoPh...36.1441C 8507:2019arXiv190911893G 8444:1990FoPh...20.1379B 8343:1983FoPh...13..481H 8152:. Berlin: Springer. 8060:2004quant.ph..8052B 8008:1990AmJPh..58..731M 7966:1990AmJPh..58.1131G 7908:1935PhRv...47..777E 7840:Griffiths, David J. 7755:2010PhRvL.104n0401B 7682:2004quant.ph..4076C 7595:1990AnPhy.202...22B 7546:1982PhRvL..48..291F 7485:Nielsen, Michael A. 7379:2018Natur.557..212B 6785:Quantum nonlocality 6671:Bohm interpretation 6464:Bell's publications 5724:will instead yield 5423: 5408: 5393: 4683:, and likewise for 2588:{\displaystyle 3/4} 325:, and likewise for 123:remain unresolved. 13674:1964 introductions 13580:Forest/Rigetti QCS 13316:quantum logic gate 13102:Bernstein–Vazirani 13089:Quantum algorithms 12964:Classical capacity 12848:Quantum processors 12831:Quantum simulation 12708:in popular culture 12490:Quantum algorithms 12338:Von Neumann–Wigner 12318:Objective collapse 12014:Old quantum theory 11647:Quantum speakables 11516:. pp. 171–81. 11494:10.1007/bf02746964 9441:Wilce, A. (2017). 9423:Notices of the AMS 9366:Gleason, Andrew M. 8677:Notices of the AMS 8452:10.1007/BF01883492 8351:10.1007/BF00729511 7417:Wolchover, Natalie 7234: 7214: 7173: 7153: 7133: 7113: 7063: 7036: 6992: 6964: 6913: 6881: 6853: 6755:Leggett inequality 6702:superdeterministic 6505: 6447:special relativity 6267: 6159:Spekkens toy model 6115: 6080: 6044: 6024: 6004: 5962: 5912: 5874: 5842: 5810: 5772: 5740:{\displaystyle -1} 5737: 5714: 5661: 5636:{\displaystyle +1} 5633: 5610: 5553:{\displaystyle +1} 5550: 5527: 5510:{\displaystyle +1} 5507: 5487:{\displaystyle -1} 5484: 5461: 5409: 5394: 5379: 5221: 5174: 5144: 5117: 5093:{\displaystyle +1} 5090: 5070:{\displaystyle -1} 5067: 5044: 4942: 4915: 4887: 4860: 4833: 4806: 4779: 4726: 4676:{\displaystyle +1} 4673: 4650: 4597: 4572:{\displaystyle +1} 4569: 4546: 4519: 4492: 4467:{\displaystyle -1} 4464: 4444:{\displaystyle +1} 4441: 4418: 4391: 4364: 4337: 4309: 4281: 4199:Daniel Greenberger 4170: 4138: 4109: 4080: 4027: 3914: 3852: 3823: 3794: 3765: 3615: 3586: 3553: 3524: 3504: 3475: 3455: 3362: 3318: 3270: 3241: 3106: 3075: 3016: 2966: 2904: 2860: 2771: 2742: 2708:{\displaystyle -1} 2705: 2685:{\displaystyle +1} 2682: 2663:spin singlet state 2634: 2585: 2557: 2537: 2513: 2493: 2469: 2421: 2401: 2381: 2361: 2341: 2321: 2301: 2278: 2250: 2095: 1882: 1759: 1750: 1648: 1621: 1590: 1581: 1514: 1486: 1458: 1342: 1315: 1255: 1100: 994: 971: 909: 853: 810: 770: 747: 720: 693: 499: 475:{\displaystyle +1} 472: 452:{\displaystyle +1} 449: 426: 396: 369: 342: 318:{\displaystyle -1} 315: 295:{\displaystyle +1} 292: 269: 238: 211: 184: 157: 56:, the idea that a 27:Theorem in physics 13636: 13635: 13547: 13546: 13444:Linear optical QC 13225:Quantum supremacy 13179:complexity theory 13132:Quantum annealing 13083: 13082: 13020:Superdense coding 12809:Quantum computing 12751: 12750: 12725:Quantum mysticism 12703:Schrödinger's cat 12634:Quantum simulator 12604:Quantum metrology 12532:Quantum computing 12495:Quantum amplifier 12472:Quantum spacetime 12437:Quantum cosmology 12427:Quantum chemistry 12127:Scattering theory 12075:Zero-point energy 12070:Degenerate levels 11978:Quantum mechanics 11885:978-0-198-24861-3 11834:978-0-262-01506-6 11726:(11): 1665–1668. 11702:978-0-521-80349-6 11217:978-3-319-41284-9 10936:978-90-481-4044-2 10911:. pp. 1–27. 10585:978-0-691-03669-4 10549:978-3-319-38985-1 10157:(7575): 682–686. 9920:10.1119/1.1498860 9843:(6769): 515–519. 9629:978-0-19-874299-9 9412:Chernoff, Paul R. 9326:Mackey, George W. 9263:978-0-486-65969-5 9094:978-0-387-94726-6 9013:(12): 1881–1927. 8884:Reichenbach, Hans 8754:Physical Review A 8698:Physical Review A 8438:(11): 1379–1387. 8194:978-0-486-60269-1 8146:von Neumann, John 8123:978-3-540-20606-4 8068:10.26421/QIC5.7-2 7629:978-0-192-65027-6 7582:Annals of Physics 7577:Caves, Carlton M. 7504:978-1-107-00217-3 7363:(7704): 212–216. 7334:. October 4, 2022 7330:(Press release). 7176:{\displaystyle +} 7156:{\displaystyle +} 7136:{\displaystyle 0} 7116:{\displaystyle -} 6442:Gleason's theorem 6438:Andrew M. Gleason 6139:free will theorem 6100:Free will theorem 6094:Free will theorem 5530:{\displaystyle 1} 4244: 4243: 4188:GHZ–Mermin (1990) 4164: 4135: 4106: 4075: 4071: 4054: 4050: 4022: 4018: 4000: 3985: 3961: 3946: 3899: 3884: 3849: 3820: 3791: 3756: 3741: 3706: 3691: 3667: 3652: 3612: 3583: 3550: 3527:{\displaystyle B} 3501: 3478:{\displaystyle A} 3434: 3394: 3350: 3306: 3226: 3199: 3153: 3138: 3063: 3048: 3007: 2992: 2951: 2936: 2901: 2886: 2854: 2839: 2818: 2803: 2768: 2739: 2622: 2616: 2560:{\displaystyle b} 2540:{\displaystyle a} 2516:{\displaystyle y} 2496:{\displaystyle x} 2424:{\displaystyle b} 2404:{\displaystyle a} 2384:{\displaystyle y} 2371:to Alice and bit 2364:{\displaystyle x} 2344:{\displaystyle y} 2324:{\displaystyle x} 2276: 2248: 2089: 2088: 2039: 2038: 1992: 1991: 1945: 1944: 1877: 1876: 1831: 1824: 1823: 1693: 1453: 1452: 74:John Stewart Bell 46:quantum mechanics 18:Bell inequalities 16:(Redirected from 13686: 13626: 13625: 13616: 13615: 13422: 13421: 13352:error correction 13281:computing models 13247:Relaxation times 13137:Quantum counting 13026: 13025: 12974:quantum capacity 12921:No-teleportation 12906:No-communication 12778: 12771: 12764: 12755: 12754: 12741: 12740: 12452:Quantum geometry 12447:Quantum dynamics 12304:Superdeterminism 12236:Rarita–Schwinger 12185:Matrix mechanics 12040:Bra–ket notation 11971: 11964: 11957: 11948: 11947: 11943: 11925: 11916:"Bell's theorem" 11897: 11867: 11838: 11814: 11780: 11759: 11714: 11687: 11685: 11656:"Bell's theorem" 11650: 11641: 11639: 11638: 11620: 11595:(6): 4381–4395. 11586: 11576: 11574: 11573: 11567: 11536: 11526: 11517: 11505: 11475: 11473: 11440: 11438: 11396: 11393:10.1063/1.880968 11367: 11332:Mermin, N. David 11327: 11303: 11294: 11282: 11273: 11249: 11248: 11246: 11245: 11194:'t Hooft, Gerard 11190: 11184: 11183: 11181: 11180: 11146: 11120: 11114: 11113: 11079: 11057: 11051: 11050: 11016: 10986: 10980: 10979: 10977: 10975:quant-ph/0301059 10961: 10955: 10954: 10952: 10951: 10945: 10920: 10910: 10899: 10893: 10892: 10866: 10864:quant-ph/9906007 10837: 10831: 10830: 10802: 10787:Brown, Harvey R. 10783: 10774: 10773: 10771: 10770: 10748: 10742: 10741: 10707: 10698:(4): 2835–2844. 10686:Hohenberg, P. C. 10682: 10676: 10675: 10657: 10655:quant-ph/9807055 10632: 10626: 10625: 10604: 10598: 10597: 10568: 10562: 10561: 10533: 10517: 10511: 10510: 10464: 10458: 10457: 10431: 10412:Zeilinger, Anton 10407: 10401: 10400: 10398: 10397: 10382: 10376: 10375: 10373: 10339: 10333: 10332: 10298: 10276: 10270: 10269: 10259: 10233: 10207: 10201: 10200: 10166: 10144: 10138: 10137: 10135: 10133: 10116: 10110: 10109: 10091: 10057: 10051: 10050: 10016: 9994: 9988: 9987: 9961: 9941: 9932: 9931: 9905: 9903:quant-ph/0205171 9883: 9877: 9876: 9857:10.1038/35000514 9830: 9824: 9823: 9821: 9787: 9781: 9780: 9778: 9767: 9761: 9760: 9743:(938): 938–941. 9732: 9716: 9710: 9709: 9707: 9706: 9686: 9680: 9679: 9643: 9634: 9633: 9613: 9607: 9606: 9581:(4): L175–L178. 9561: 9555: 9554: 9529: 9523: 9522: 9496: 9476: 9468:Mermin, N. David 9464: 9453: 9452: 9438: 9432: 9431: 9430:(10): 1253–1259. 9419: 9408: 9402: 9401: 9391: 9362: 9356: 9355: 9322: 9316: 9315: 9282: 9276: 9275: 9246: 9240: 9239: 9213: 9191: 9185: 9184: 9157:Einstein, Albert 9153: 9147: 9146: 9121:Zeilinger, Anton 9105: 9099: 9098: 9072: 9063: 9062: 9060: 9059: 9053: 9030: 9004: 8995: 8989: 8988: 8962: 8953:(9): 1007–1020. 8941:Mermin, N. David 8937: 8931: 8930: 8909: 8900: 8899: 8880: 8874: 8873: 8855: 8837: 8811: 8805: 8804: 8770: 8768:quant-ph/0401052 8745: 8739: 8738: 8705:(8): 4277–4281. 8692: 8686: 8685: 8673: 8657: 8651: 8650: 8648: 8647: 8630: 8624: 8623: 8621: 8620: 8603: 8597: 8596: 8570: 8568:quant-ph/0604079 8541: 8535: 8534: 8500: 8491:(6): 1445–1451. 8478: 8472: 8471: 8422: 8416: 8415: 8377: 8371: 8370: 8323:Heywood, Peter; 8320: 8314: 8313: 8269:Redhead, Michael 8265: 8259: 8258: 8223: 8217: 8216: 8214: 8206:S. Hirzel Verlag 8204:(2nd ed.). 8198: 8185:Robertson, H. P. 8183:. Translated by 8173: 8167: 8166: 8163:Beyer, Robert T. 8161:. Translated by 8153: 8142: 8136: 8135: 8098: 8092: 8091: 8078: 8072: 8071: 8053: 8051:quant-ph/0408052 8030:Brassard, Gilles 8026: 8020: 8019: 7990:Mermin, N. David 7986: 7980: 7979: 7977: 7928: 7922: 7921: 7919: 7874: 7868: 7867: 7836: 7830: 7829: 7809: 7797: 7791: 7790: 7748: 7726: 7720: 7719: 7675: 7673:quant-ph/0404076 7648: 7642: 7641: 7613: 7607: 7606: 7572: 7566: 7565: 7523: 7517: 7516: 7489:Chuang, Isaac L. 7481: 7468: 7467: 7458:Zalta, Edward N. 7454:"Bell's Theorem" 7446: 7437: 7436: 7434: 7433: 7413: 7407: 7406: 7372: 7350: 7344: 7343: 7341: 7339: 7318: 7312: 7311: 7282: 7265: 7259: 7253: 7243: 7241: 7240: 7235: 7223: 7221: 7220: 7215: 7182: 7180: 7179: 7174: 7162: 7160: 7159: 7154: 7142: 7140: 7139: 7134: 7122: 7120: 7119: 7114: 7089: 7083: 7080: 7074: 7072: 7070: 7069: 7064: 7062: 7061: 7045: 7043: 7042: 7037: 7029: 7028: 7019: 7001: 6999: 6998: 6993: 6985: 6973: 6971: 6970: 6965: 6963: 6962: 6957: 6945: 6934: 6922: 6920: 6919: 6914: 6890: 6888: 6887: 6882: 6880: 6879: 6867:) Hilbert space 6863:belonging to a ( 6862: 6860: 6859: 6854: 6846: 6829:John von Neumann 6817: 6811: 6807: 6731: 6726: 6725: 6691:Superdeterminism 6685:Superdeterminism 6323:Hans Reichenbach 6319:John von Neumann 6276: 6274: 6273: 6268: 6260: 6259: 6247: 6246: 6234: 6233: 6203: 6202: 6124: 6122: 6121: 6116: 6089: 6087: 6086: 6081: 6053: 6051: 6050: 6045: 6033: 6031: 6030: 6025: 6013: 6011: 6010: 6005: 5971: 5969: 5968: 5963: 5921: 5919: 5918: 5913: 5883: 5881: 5880: 5875: 5851: 5849: 5848: 5843: 5819: 5817: 5816: 5811: 5781: 5779: 5778: 5773: 5746: 5744: 5743: 5738: 5723: 5721: 5720: 5715: 5713: 5712: 5700: 5699: 5687: 5686: 5670: 5668: 5667: 5662: 5654: 5642: 5640: 5639: 5634: 5619: 5617: 5616: 5611: 5596: 5595: 5586: 5585: 5576: 5575: 5559: 5557: 5556: 5551: 5536: 5534: 5533: 5528: 5516: 5514: 5513: 5508: 5493: 5491: 5490: 5485: 5470: 5468: 5467: 5462: 5456: 5455: 5446: 5445: 5436: 5435: 5422: 5417: 5407: 5402: 5392: 5387: 5378: 5377: 5368: 5367: 5358: 5357: 5342: 5341: 5332: 5331: 5322: 5321: 5306: 5305: 5296: 5295: 5286: 5285: 5270: 5269: 5260: 5259: 5250: 5249: 5230: 5228: 5227: 5222: 5220: 5219: 5210: 5209: 5200: 5199: 5183: 5181: 5180: 5175: 5173: 5172: 5153: 5151: 5150: 5145: 5143: 5142: 5126: 5124: 5123: 5118: 5116: 5115: 5099: 5097: 5096: 5091: 5076: 5074: 5073: 5068: 5053: 5051: 5050: 5045: 5036: 5035: 5023: 5022: 5010: 5009: 4997: 4996: 4984: 4983: 4971: 4970: 4951: 4949: 4948: 4943: 4941: 4940: 4924: 4922: 4921: 4916: 4914: 4913: 4896: 4894: 4893: 4888: 4886: 4885: 4869: 4867: 4866: 4861: 4859: 4858: 4842: 4840: 4839: 4834: 4832: 4831: 4815: 4813: 4812: 4807: 4805: 4804: 4788: 4786: 4785: 4780: 4778: 4777: 4765: 4764: 4752: 4751: 4735: 4733: 4732: 4727: 4725: 4724: 4712: 4711: 4699: 4698: 4682: 4680: 4679: 4674: 4660:with eigenvalue 4659: 4657: 4656: 4651: 4649: 4648: 4636: 4635: 4623: 4622: 4606: 4604: 4603: 4598: 4590: 4578: 4576: 4575: 4570: 4555: 4553: 4552: 4547: 4545: 4544: 4528: 4526: 4525: 4520: 4518: 4517: 4501: 4499: 4498: 4493: 4485: 4473: 4471: 4470: 4465: 4450: 4448: 4447: 4442: 4427: 4425: 4424: 4419: 4417: 4416: 4400: 4398: 4397: 4392: 4390: 4389: 4373: 4371: 4370: 4365: 4363: 4362: 4346: 4344: 4343: 4338: 4330: 4318: 4316: 4315: 4310: 4302: 4291:where as above, 4290: 4288: 4287: 4282: 4267: 4253: 4245: 4239: 4235: 4224: 4203:Michael A. Horne 4179: 4177: 4176: 4171: 4166: 4165: 4157: 4147: 4145: 4144: 4139: 4137: 4136: 4128: 4118: 4116: 4115: 4110: 4108: 4107: 4099: 4089: 4087: 4086: 4081: 4076: 4067: 4066: 4055: 4046: 4045: 4036: 4034: 4033: 4028: 4023: 4014: 4013: 4002: 4001: 3993: 3987: 3986: 3978: 3963: 3962: 3954: 3948: 3947: 3939: 3923: 3921: 3920: 3915: 3901: 3900: 3892: 3886: 3885: 3877: 3861: 3859: 3858: 3853: 3851: 3850: 3842: 3832: 3830: 3829: 3824: 3822: 3821: 3813: 3803: 3801: 3800: 3795: 3793: 3792: 3784: 3774: 3772: 3771: 3766: 3758: 3757: 3749: 3743: 3742: 3734: 3716: 3708: 3707: 3699: 3693: 3692: 3684: 3669: 3668: 3660: 3654: 3653: 3645: 3636: 3624: 3622: 3621: 3616: 3614: 3613: 3605: 3595: 3593: 3592: 3587: 3585: 3584: 3576: 3562: 3560: 3559: 3554: 3552: 3551: 3543: 3533: 3531: 3530: 3525: 3513: 3511: 3510: 3505: 3503: 3502: 3494: 3484: 3482: 3481: 3476: 3464: 3462: 3461: 3456: 3436: 3435: 3427: 3396: 3395: 3387: 3371: 3369: 3368: 3363: 3352: 3351: 3343: 3327: 3325: 3324: 3319: 3308: 3307: 3299: 3279: 3277: 3276: 3271: 3250: 3248: 3247: 3242: 3228: 3227: 3219: 3201: 3200: 3192: 3155: 3154: 3146: 3140: 3139: 3131: 3115: 3113: 3112: 3107: 3084: 3082: 3081: 3076: 3065: 3064: 3056: 3050: 3049: 3041: 3025: 3023: 3022: 3017: 3009: 3008: 3000: 2994: 2993: 2985: 2975: 2973: 2972: 2967: 2953: 2952: 2944: 2938: 2937: 2929: 2913: 2911: 2910: 2905: 2903: 2902: 2894: 2888: 2887: 2879: 2869: 2867: 2866: 2861: 2856: 2855: 2847: 2841: 2840: 2832: 2820: 2819: 2811: 2805: 2804: 2796: 2780: 2778: 2777: 2772: 2770: 2769: 2761: 2751: 2749: 2748: 2743: 2741: 2740: 2732: 2714: 2712: 2711: 2706: 2691: 2689: 2688: 2683: 2643: 2641: 2640: 2635: 2623: 2618: 2617: 2612: 2603: 2594: 2592: 2591: 2586: 2581: 2566: 2564: 2563: 2558: 2546: 2544: 2543: 2538: 2522: 2520: 2519: 2514: 2502: 2500: 2499: 2494: 2478: 2476: 2475: 2470: 2430: 2428: 2427: 2422: 2410: 2408: 2407: 2402: 2390: 2388: 2387: 2382: 2370: 2368: 2367: 2362: 2350: 2348: 2347: 2342: 2330: 2328: 2327: 2322: 2287: 2285: 2284: 2279: 2277: 2272: 2259: 2257: 2256: 2251: 2249: 2244: 2233: 2232: 2220: 2219: 2201: 2200: 2188: 2187: 2169: 2168: 2156: 2155: 2137: 2136: 2124: 2123: 2104: 2102: 2101: 2096: 2090: 2084: 2080: 2069: 2068: 2056: 2055: 2040: 2034: 2030: 2022: 2021: 2009: 2008: 1993: 1987: 1983: 1975: 1974: 1962: 1961: 1946: 1940: 1936: 1928: 1927: 1915: 1914: 1891: 1889: 1888: 1883: 1878: 1872: 1871: 1870: 1869: 1857: 1856: 1846: 1841: 1840: 1829: 1825: 1819: 1818: 1817: 1816: 1804: 1803: 1793: 1785: 1784: 1768: 1766: 1765: 1760: 1755: 1754: 1716: 1715: 1703: 1702: 1691: 1687: 1686: 1674: 1673: 1657: 1655: 1654: 1649: 1647: 1646: 1630: 1628: 1627: 1622: 1620: 1619: 1599: 1597: 1596: 1591: 1586: 1585: 1544: 1543: 1523: 1521: 1520: 1515: 1507: 1495: 1493: 1492: 1487: 1479: 1467: 1465: 1464: 1459: 1454: 1448: 1447: 1440: 1426: 1412: 1398: 1392: 1381: 1351: 1349: 1348: 1343: 1341: 1340: 1324: 1322: 1321: 1316: 1311: 1310: 1298: 1297: 1285: 1284: 1264: 1262: 1261: 1256: 1244: 1236: 1235: 1226: 1225: 1207: 1206: 1197: 1196: 1178: 1177: 1168: 1167: 1149: 1148: 1139: 1138: 1126: 1109: 1107: 1106: 1101: 1099: 1098: 1089: 1088: 1076: 1075: 1066: 1065: 1053: 1052: 1043: 1042: 1030: 1029: 1020: 1019: 1003: 1001: 1000: 995: 980: 978: 977: 972: 964: 963: 951: 950: 938: 937: 918: 916: 915: 910: 908: 907: 895: 894: 882: 881: 862: 860: 859: 854: 852: 851: 836: 835: 819: 817: 816: 811: 809: 808: 796: 795: 779: 777: 776: 771: 757:take the values 756: 754: 753: 748: 746: 745: 729: 727: 726: 721: 719: 718: 702: 700: 699: 694: 688: 687: 675: 674: 662: 661: 646: 645: 633: 632: 620: 619: 604: 603: 594: 593: 581: 580: 571: 570: 558: 557: 548: 547: 535: 534: 525: 524: 508: 506: 505: 500: 498: 497: 481: 479: 478: 473: 458: 456: 455: 450: 435: 433: 432: 427: 425: 424: 405: 403: 402: 397: 395: 394: 378: 376: 375: 370: 368: 367: 351: 349: 348: 343: 341: 340: 324: 322: 321: 316: 301: 299: 298: 293: 278: 276: 275: 270: 268: 267: 247: 245: 244: 239: 237: 236: 220: 218: 217: 212: 210: 209: 193: 191: 190: 185: 183: 182: 166: 164: 163: 158: 156: 155: 70:Hidden variables 21: 13694: 13693: 13689: 13688: 13687: 13685: 13684: 13683: 13639: 13638: 13637: 13632: 13604: 13554: 13543: 13516:Superconducting 13510: 13476: 13467:Neutral atom QC 13459:Ultracold atoms 13453: 13418:implementations 13417: 13411: 13351: 13344: 13311:Quantum circuit 13279: 13273: 13267: 13257: 13217: 13211: 13178: 13171: 13127:Hidden subgroup 13079: 13068:other protocols 13024: 13001:quantum network 12996:Quantum channel 12956: 12950: 12896:No-broadcasting 12886:Gottesman–Knill 12859: 12787: 12782: 12752: 12747: 12729: 12715:Wigner's friend 12691: 12682:Quantum gravity 12643: 12629:Quantum sensing 12609:Quantum network 12589:Quantum machine 12559:Quantum imaging 12522:Quantum circuit 12517:Quantum channel 12476: 12422:Quantum biology 12408: 12384:Elitzur–Vaidman 12359:Davisson–Germer 12342: 12294:Hidden-variable 12284:de Broglie–Bohm 12261:Interpretations 12255: 12204: 12158: 12045:Complementarity 12023: 11980: 11975: 11928: 11914: 11905: 11900: 11886: 11835: 11765:Phys. Rev. Lett 11703: 11636: 11634: 11584: 11571: 11569: 11565: 11534: 11450:Phys. Rev. Lett 11415:Phys. Rev. Lett 11356:10.1119/1.12594 11342:(10): 940–943. 11324: 11258: 11256:Further reading 11253: 11252: 11243: 11241: 11218: 11191: 11187: 11178: 11176: 11121: 11117: 11070:(7138): 871–5. 11058: 11054: 10987: 10983: 10962: 10958: 10949: 10947: 10943: 10937: 10908: 10900: 10896: 10845:Hayden, Patrick 10838: 10834: 10819: 10784: 10777: 10768: 10766: 10749: 10745: 10683: 10679: 10633: 10629: 10622: 10608:Peierls, Rudolf 10605: 10601: 10586: 10569: 10565: 10550: 10518: 10514: 10465: 10461: 10408: 10404: 10395: 10393: 10383: 10379: 10340: 10336: 10277: 10273: 10208: 10204: 10145: 10141: 10131: 10129: 10117: 10113: 10074:(7567): 14–15. 10058: 10054: 9995: 9991: 9942: 9935: 9884: 9880: 9831: 9827: 9788: 9784: 9776: 9768: 9764: 9730: 9720:Freedman, S. J. 9717: 9713: 9704: 9702: 9687: 9683: 9644: 9637: 9630: 9614: 9610: 9562: 9558: 9530: 9526: 9474: 9465: 9456: 9439: 9435: 9417: 9409: 9405: 9363: 9359: 9323: 9319: 9291:Physical Review 9283: 9279: 9264: 9247: 9243: 9192: 9188: 9154: 9150: 9135: 9106: 9102: 9095: 9073: 9066: 9057: 9055: 9051: 9028:10.1.1.482.4728 9002: 8996: 8992: 8938: 8934: 8927: 8910: 8903: 8881: 8877: 8812: 8808: 8746: 8742: 8693: 8689: 8671: 8661:Conway, John H. 8658: 8654: 8645: 8643: 8631: 8627: 8618: 8616: 8604: 8600: 8542: 8538: 8479: 8475: 8423: 8419: 8378: 8374: 8321: 8317: 8266: 8262: 8247: 8224: 8220: 8208: 8200: 8195: 8174: 8170: 8155: 8143: 8139: 8124: 8099: 8095: 8079: 8075: 8034:Broadbent, Anne 8027: 8023: 8016:10.1119/1.16503 7987: 7983: 7975:10.1119/1.16243 7932:Greenberger, D. 7929: 7925: 7902:(10): 777–780. 7895:Physical Review 7875: 7871: 7856: 7837: 7833: 7807: 7798: 7794: 7727: 7723: 7700: 7649: 7645: 7630: 7614: 7610: 7573: 7569: 7524: 7520: 7505: 7482: 7471: 7447: 7440: 7431: 7429: 7426:Quanta Magazine 7414: 7410: 7351: 7347: 7337: 7335: 7320: 7319: 7315: 7300: 7283: 7279: 7274: 7269: 7268: 7260: 7256: 7229: 7226: 7225: 7188: 7185: 7184: 7168: 7165: 7164: 7148: 7145: 7144: 7128: 7125: 7124: 7108: 7105: 7104: 7090: 7086: 7081: 7077: 7057: 7053: 7051: 7048: 7047: 7024: 7020: 7015: 7007: 7004: 7003: 6981: 6979: 6976: 6975: 6958: 6953: 6952: 6941: 6930: 6928: 6925: 6924: 6908: 6905: 6904: 6875: 6874: 6872: 6869: 6868: 6842: 6840: 6837: 6836: 6818: 6814: 6808: 6804: 6799: 6794: 6765:Mermin's device 6727: 6720: 6717: 6709:Gerard 't Hooft 6693: 6687: 6662: 6638: 6603: 6594: 6588: 6586:Interpretations 6576:Anton Zeilinger 6535:first Bell test 6527:Stuart Freedman 6511: 6501: 6492: 6466: 6426:Chien-Shiung Wu 6388:separated from 6311: 6303:Main articles: 6301: 6296: 6279:Robert Spekkens 6255: 6251: 6242: 6238: 6226: 6222: 6195: 6191: 6189: 6186: 6185: 6170:Reinhard Werner 6165: 6157:Main articles: 6155: 6110: 6107: 6106: 6102: 6096: 6075: 6072: 6071: 6039: 6036: 6035: 6019: 6016: 6015: 5999: 5996: 5995: 5988: 5982: 5927: 5924: 5923: 5889: 5886: 5885: 5857: 5854: 5853: 5825: 5822: 5821: 5787: 5784: 5783: 5755: 5752: 5751: 5729: 5726: 5725: 5708: 5704: 5695: 5691: 5682: 5678: 5676: 5673: 5672: 5650: 5648: 5645: 5644: 5625: 5622: 5621: 5591: 5587: 5581: 5577: 5571: 5567: 5565: 5562: 5561: 5542: 5539: 5538: 5522: 5519: 5518: 5499: 5496: 5495: 5476: 5473: 5472: 5451: 5447: 5441: 5437: 5431: 5427: 5418: 5413: 5403: 5398: 5388: 5383: 5373: 5369: 5363: 5359: 5353: 5349: 5337: 5333: 5327: 5323: 5317: 5313: 5301: 5297: 5291: 5287: 5281: 5277: 5265: 5261: 5255: 5251: 5245: 5241: 5236: 5233: 5232: 5215: 5211: 5205: 5201: 5195: 5191: 5189: 5186: 5185: 5168: 5164: 5162: 5159: 5158: 5138: 5134: 5132: 5129: 5128: 5111: 5107: 5105: 5102: 5101: 5082: 5079: 5078: 5059: 5056: 5055: 5031: 5027: 5018: 5014: 5005: 5001: 4992: 4988: 4979: 4975: 4966: 4962: 4957: 4954: 4953: 4936: 4932: 4930: 4927: 4926: 4909: 4905: 4903: 4900: 4899: 4881: 4877: 4875: 4872: 4871: 4854: 4850: 4848: 4845: 4844: 4827: 4823: 4821: 4818: 4817: 4800: 4796: 4794: 4791: 4790: 4773: 4769: 4760: 4756: 4747: 4743: 4741: 4738: 4737: 4720: 4716: 4707: 4703: 4694: 4690: 4688: 4685: 4684: 4665: 4662: 4661: 4644: 4640: 4631: 4627: 4618: 4614: 4612: 4609: 4608: 4586: 4584: 4581: 4580: 4561: 4558: 4557: 4540: 4536: 4534: 4531: 4530: 4513: 4509: 4507: 4504: 4503: 4481: 4479: 4476: 4475: 4456: 4453: 4452: 4433: 4430: 4429: 4412: 4408: 4406: 4403: 4402: 4385: 4381: 4379: 4376: 4375: 4358: 4354: 4352: 4349: 4348: 4326: 4324: 4321: 4320: 4298: 4296: 4293: 4292: 4263: 4249: 4234: 4220: 4218: 4215: 4214: 4207:Anton Zeilinger 4196: 4190: 4156: 4155: 4153: 4150: 4149: 4127: 4126: 4124: 4121: 4120: 4098: 4097: 4095: 4092: 4091: 4065: 4044: 4042: 4039: 4038: 4012: 3992: 3991: 3977: 3976: 3953: 3952: 3938: 3937: 3929: 3926: 3925: 3891: 3890: 3876: 3875: 3867: 3864: 3863: 3841: 3840: 3838: 3835: 3834: 3812: 3811: 3809: 3806: 3805: 3783: 3782: 3780: 3777: 3776: 3748: 3747: 3733: 3732: 3712: 3698: 3697: 3683: 3682: 3659: 3658: 3644: 3643: 3632: 3630: 3627: 3626: 3604: 3603: 3601: 3598: 3597: 3575: 3574: 3572: 3569: 3568: 3542: 3541: 3539: 3536: 3535: 3519: 3516: 3515: 3493: 3492: 3490: 3487: 3486: 3470: 3467: 3466: 3426: 3425: 3386: 3385: 3377: 3374: 3373: 3342: 3341: 3333: 3330: 3329: 3298: 3297: 3289: 3286: 3285: 3256: 3253: 3252: 3218: 3217: 3191: 3190: 3145: 3144: 3130: 3129: 3121: 3118: 3117: 3101: 3098: 3097: 3055: 3054: 3040: 3039: 3031: 3028: 3027: 2999: 2998: 2984: 2983: 2981: 2978: 2977: 2943: 2942: 2928: 2927: 2919: 2916: 2915: 2893: 2892: 2878: 2877: 2875: 2872: 2871: 2846: 2845: 2831: 2830: 2810: 2809: 2795: 2794: 2786: 2783: 2782: 2760: 2759: 2757: 2754: 2753: 2731: 2730: 2728: 2725: 2724: 2697: 2694: 2693: 2674: 2671: 2670: 2654: 2649: 2611: 2604: 2602: 2600: 2597: 2596: 2577: 2572: 2569: 2568: 2552: 2549: 2548: 2532: 2529: 2528: 2508: 2505: 2504: 2488: 2485: 2484: 2436: 2433: 2432: 2416: 2413: 2412: 2396: 2393: 2392: 2376: 2373: 2372: 2356: 2353: 2352: 2336: 2333: 2332: 2316: 2313: 2312: 2290:Tsirelson bound 2271: 2266: 2263: 2262: 2243: 2228: 2224: 2215: 2211: 2196: 2192: 2183: 2179: 2164: 2160: 2151: 2147: 2132: 2128: 2119: 2115: 2110: 2107: 2106: 2079: 2064: 2060: 2051: 2047: 2029: 2017: 2013: 2004: 2000: 1982: 1970: 1966: 1957: 1953: 1935: 1923: 1919: 1910: 1906: 1901: 1898: 1897: 1865: 1861: 1852: 1848: 1847: 1845: 1836: 1832: 1812: 1808: 1799: 1795: 1794: 1792: 1780: 1776: 1774: 1771: 1770: 1749: 1748: 1743: 1737: 1736: 1731: 1721: 1720: 1711: 1707: 1698: 1694: 1682: 1678: 1669: 1665: 1663: 1660: 1659: 1642: 1638: 1636: 1633: 1632: 1615: 1611: 1609: 1606: 1605: 1580: 1579: 1571: 1565: 1564: 1559: 1549: 1548: 1539: 1535: 1533: 1530: 1529: 1503: 1501: 1498: 1497: 1475: 1473: 1470: 1469: 1436: 1422: 1408: 1394: 1393: 1391: 1377: 1375: 1372: 1371: 1336: 1332: 1330: 1327: 1326: 1306: 1302: 1293: 1289: 1280: 1276: 1274: 1271: 1270: 1267:CHSH inequality 1240: 1231: 1227: 1221: 1217: 1202: 1198: 1192: 1188: 1173: 1169: 1163: 1159: 1144: 1140: 1134: 1130: 1122: 1120: 1117: 1116: 1094: 1090: 1084: 1080: 1071: 1067: 1061: 1057: 1048: 1044: 1038: 1034: 1025: 1021: 1015: 1011: 1009: 1006: 1005: 986: 983: 982: 959: 955: 946: 942: 933: 929: 924: 921: 920: 903: 899: 890: 886: 877: 873: 868: 865: 864: 847: 843: 831: 827: 825: 822: 821: 804: 800: 791: 787: 785: 782: 781: 762: 759: 758: 741: 737: 735: 732: 731: 714: 710: 708: 705: 704: 683: 679: 670: 666: 657: 653: 641: 637: 628: 624: 615: 611: 599: 595: 589: 585: 576: 572: 566: 562: 553: 549: 543: 539: 530: 526: 520: 516: 514: 511: 510: 493: 489: 487: 484: 483: 482:for a property 464: 461: 460: 441: 438: 437: 420: 416: 414: 411: 410: 390: 386: 384: 381: 380: 363: 359: 357: 354: 353: 336: 332: 330: 327: 326: 307: 304: 303: 284: 281: 280: 263: 259: 257: 254: 253: 232: 228: 226: 223: 222: 205: 201: 199: 196: 195: 178: 174: 172: 169: 168: 151: 147: 145: 142: 141: 129: 104:Stuart Freedman 89:Bell inequality 62:physical fields 35: 28: 23: 22: 15: 12: 11: 5: 13692: 13682: 13681: 13679:No-go theorems 13676: 13671: 13666: 13661: 13656: 13651: 13634: 13633: 13631: 13630: 13620: 13609: 13606: 13605: 13603: 13602: 13600:many others... 13597: 13592: 13587: 13582: 13573: 13559: 13557: 13549: 13548: 13545: 13544: 13542: 13541: 13536: 13531: 13526: 13520: 13518: 13512: 13511: 13509: 13508: 13503: 13498: 13493: 13487: 13485: 13478: 13477: 13475: 13474: 13472:Trapped-ion QC 13469: 13463: 13461: 13455: 13454: 13452: 13451: 13446: 13441: 13436: 13430: 13428: 13426:Quantum optics 13419: 13413: 13412: 13410: 13409: 13404: 13403: 13402: 13395: 13390: 13385: 13380: 13375: 13370: 13365: 13356: 13354: 13346: 13345: 13343: 13342: 13337: 13332: 13331: 13330: 13320: 13319: 13318: 13308: 13307: 13306: 13296: 13291: 13285: 13283: 13275: 13274: 13272: 13271: 13270: 13269: 13265: 13259: 13255: 13244: 13243: 13242: 13232: 13230:Quantum volume 13227: 13221: 13219: 13213: 13212: 13210: 13209: 13204: 13199: 13194: 13189: 13183: 13181: 13173: 13172: 13170: 13169: 13164: 13159: 13154: 13149: 13144: 13139: 13134: 13129: 13124: 13119: 13114: 13109: 13107:Boson sampling 13104: 13099: 13093: 13091: 13085: 13084: 13081: 13080: 13078: 13077: 13072: 13071: 13070: 13065: 13060: 13050: 13045: 13040: 13034: 13032: 13023: 13022: 13017: 13016: 13015: 13005: 13004: 13003: 12993: 12988: 12983: 12978: 12977: 12976: 12971: 12960: 12958: 12952: 12951: 12949: 12948: 12943: 12941:Solovay–Kitaev 12938: 12933: 12928: 12923: 12918: 12913: 12908: 12903: 12898: 12893: 12888: 12883: 12878: 12873: 12867: 12865: 12861: 12860: 12858: 12857: 12856: 12855: 12845: 12844: 12843: 12833: 12828: 12823: 12818: 12817: 12816: 12806: 12801: 12795: 12793: 12789: 12788: 12781: 12780: 12773: 12766: 12758: 12749: 12748: 12746: 12745: 12734: 12731: 12730: 12728: 12727: 12722: 12717: 12712: 12711: 12710: 12699: 12697: 12693: 12692: 12690: 12689: 12684: 12679: 12678: 12677: 12667: 12662: 12660:Casimir effect 12657: 12651: 12649: 12645: 12644: 12642: 12641: 12636: 12631: 12626: 12621: 12619:Quantum optics 12616: 12611: 12606: 12601: 12596: 12591: 12586: 12581: 12576: 12571: 12566: 12561: 12556: 12551: 12546: 12541: 12540: 12539: 12529: 12524: 12519: 12514: 12513: 12512: 12502: 12497: 12492: 12486: 12484: 12478: 12477: 12475: 12474: 12469: 12464: 12459: 12454: 12449: 12444: 12439: 12434: 12429: 12424: 12418: 12416: 12410: 12409: 12407: 12406: 12401: 12396: 12394:Quantum eraser 12391: 12386: 12381: 12376: 12371: 12366: 12361: 12356: 12350: 12348: 12344: 12343: 12341: 12340: 12335: 12330: 12325: 12320: 12315: 12310: 12309: 12308: 12307: 12306: 12291: 12286: 12281: 12276: 12271: 12265: 12263: 12257: 12256: 12254: 12253: 12248: 12243: 12238: 12233: 12228: 12223: 12218: 12212: 12210: 12206: 12205: 12203: 12202: 12197: 12192: 12187: 12182: 12177: 12172: 12166: 12164: 12160: 12159: 12157: 12156: 12155: 12154: 12149: 12139: 12134: 12129: 12124: 12119: 12114: 12109: 12104: 12099: 12094: 12089: 12084: 12079: 12078: 12077: 12072: 12067: 12062: 12052: 12050:Density matrix 12047: 12042: 12037: 12031: 12029: 12025: 12024: 12022: 12021: 12016: 12011: 12006: 12005: 12004: 11994: 11988: 11986: 11982: 11981: 11974: 11973: 11966: 11959: 11951: 11945: 11944: 11926: 11912: 11904: 11903:External links 11901: 11899: 11898: 11884: 11868: 11850:(4): 365–391. 11839: 11833: 11815: 11771:(15): 150404. 11760: 11715: 11701: 11688: 11651: 11642: 11577: 11545:(5): 158–181. 11527: 11518: 11506: 11488:(8): 345–348. 11476: 11441: 11421:(7): 460–463. 11402: 11398: 11397: 11368: 11328: 11322: 11304: 11295: 11283: 11274: 11266:Aczel, Amir D. 11257: 11254: 11251: 11250: 11216: 11185: 11115: 11052: 10993:(2015-03-03). 10981: 10956: 10935: 10918:10.1.1.46.1264 10894: 10841:Deutsch, David 10832: 10817: 10775: 10743: 10677: 10648:(4): 571–587. 10627: 10620: 10599: 10584: 10563: 10548: 10512: 10477:(42): 424011. 10459: 10422:(3): 222–230. 10402: 10377: 10334: 10289:(25): 250401. 10271: 10224:(25): 250402. 10202: 10139: 10126:New York Times 10111: 10052: 10007:(17): 170404. 9989: 9952:(42): 424003. 9933: 9896:(9): 903–910. 9878: 9825: 9804:(25): 1804–7. 9782: 9762: 9724:Clauser, J. F. 9711: 9692:(2012-01-30). 9681: 9654:(3): 447–452. 9635: 9628: 9608: 9556: 9533:Shimony, Abner 9524: 9487:(3): 803–815. 9454: 9433: 9403: 9382:(4): 885–893. 9357: 9338:(8P2): 45–57. 9317: 9277: 9262: 9254:Quantum Theory 9241: 9186: 9167:(3): 349–382. 9148: 9133: 9100: 9093: 9064: 8990: 8932: 8925: 8901: 8875: 8806: 8740: 8687: 8652: 8625: 8598: 8536: 8473: 8417: 8396:10.1086/289140 8390:(4): 578–602. 8372: 8337:(5): 481–499. 8315: 8285:(1): 119–160. 8260: 8245: 8218: 8193: 8168: 8137: 8122: 8114:10.1007/b12915 8102:Hilbert, David 8093: 8073: 8044:(7): 538–550. 8021: 8002:(8): 731–734. 7981: 7923: 7888:(1935-05-15). 7869: 7854: 7831: 7820:(3): 195–200. 7792: 7739:(14): 140401. 7721: 7698: 7643: 7628: 7608: 7567: 7540:(5): 291–295. 7518: 7503: 7469: 7450:Shimony, Abner 7438: 7419:(2017-02-07). 7408: 7345: 7313: 7298: 7276: 7275: 7273: 7270: 7267: 7266: 7254: 7233: 7213: 7210: 7207: 7204: 7201: 7198: 7195: 7192: 7172: 7152: 7132: 7112: 7084: 7075: 7060: 7056: 7035: 7032: 7027: 7023: 7018: 7014: 7011: 6991: 6988: 6984: 6961: 6956: 6951: 6948: 6944: 6940: 6937: 6933: 6912: 6878: 6852: 6849: 6845: 6812: 6801: 6800: 6798: 6795: 6793: 6792: 6787: 6782: 6777: 6772: 6767: 6762: 6757: 6752: 6747: 6740: 6734: 6733: 6732: 6729:physics portal 6716: 6713: 6689:Main article: 6686: 6683: 6661: 6658: 6637: 6634: 6618:Rudolf Peierls 6602: 6599: 6590:Main article: 6587: 6584: 6507:Main article: 6491: 6488: 6465: 6462: 6398: 6397: 6300: 6297: 6295: 6292: 6266: 6263: 6258: 6254: 6250: 6245: 6241: 6237: 6232: 6229: 6225: 6221: 6218: 6215: 6212: 6209: 6206: 6201: 6198: 6194: 6182:tensor-product 6154: 6151: 6114: 6098:Main article: 6095: 6092: 6079: 6043: 6023: 6003: 5984:Main article: 5981: 5978: 5961: 5958: 5955: 5952: 5949: 5946: 5943: 5940: 5937: 5934: 5931: 5911: 5908: 5905: 5902: 5899: 5896: 5893: 5873: 5870: 5867: 5864: 5861: 5841: 5838: 5835: 5832: 5829: 5809: 5806: 5803: 5800: 5797: 5794: 5791: 5771: 5768: 5765: 5762: 5759: 5736: 5733: 5711: 5707: 5703: 5698: 5694: 5690: 5685: 5681: 5660: 5657: 5653: 5632: 5629: 5609: 5605: 5602: 5599: 5594: 5590: 5584: 5580: 5574: 5570: 5549: 5546: 5526: 5506: 5503: 5483: 5480: 5460: 5454: 5450: 5444: 5440: 5434: 5430: 5426: 5421: 5416: 5412: 5406: 5401: 5397: 5391: 5386: 5382: 5376: 5372: 5366: 5362: 5356: 5352: 5348: 5345: 5340: 5336: 5330: 5326: 5320: 5316: 5312: 5309: 5304: 5300: 5294: 5290: 5284: 5280: 5276: 5273: 5268: 5264: 5258: 5254: 5248: 5244: 5240: 5218: 5214: 5208: 5204: 5198: 5194: 5171: 5167: 5141: 5137: 5114: 5110: 5089: 5086: 5066: 5063: 5043: 5039: 5034: 5030: 5026: 5021: 5017: 5013: 5008: 5004: 5000: 4995: 4991: 4987: 4982: 4978: 4974: 4969: 4965: 4961: 4939: 4935: 4912: 4908: 4884: 4880: 4857: 4853: 4830: 4826: 4803: 4799: 4776: 4772: 4768: 4763: 4759: 4755: 4750: 4746: 4723: 4719: 4715: 4710: 4706: 4702: 4697: 4693: 4672: 4669: 4647: 4643: 4639: 4634: 4630: 4626: 4621: 4617: 4596: 4593: 4589: 4568: 4565: 4543: 4539: 4516: 4512: 4491: 4488: 4484: 4463: 4460: 4440: 4437: 4415: 4411: 4388: 4384: 4361: 4357: 4336: 4333: 4329: 4308: 4305: 4301: 4280: 4276: 4273: 4270: 4266: 4262: 4259: 4256: 4252: 4248: 4242: 4238: 4233: 4230: 4227: 4223: 4194:GHZ experiment 4192:Main article: 4189: 4186: 4169: 4163: 4160: 4134: 4131: 4105: 4102: 4079: 4074: 4070: 4064: 4061: 4058: 4053: 4049: 4026: 4021: 4017: 4011: 4008: 4005: 3999: 3996: 3990: 3984: 3981: 3975: 3972: 3969: 3966: 3960: 3957: 3951: 3945: 3942: 3936: 3933: 3913: 3910: 3907: 3904: 3898: 3895: 3889: 3883: 3880: 3874: 3871: 3848: 3845: 3819: 3816: 3790: 3787: 3764: 3761: 3755: 3752: 3746: 3740: 3737: 3731: 3728: 3725: 3722: 3719: 3715: 3711: 3705: 3702: 3696: 3690: 3687: 3681: 3678: 3675: 3672: 3666: 3663: 3657: 3651: 3648: 3642: 3639: 3635: 3611: 3608: 3582: 3579: 3549: 3546: 3523: 3500: 3497: 3474: 3454: 3451: 3448: 3445: 3442: 3439: 3433: 3430: 3424: 3421: 3417: 3414: 3411: 3408: 3405: 3402: 3399: 3393: 3390: 3384: 3381: 3361: 3358: 3355: 3349: 3346: 3340: 3337: 3317: 3314: 3311: 3305: 3302: 3296: 3293: 3269: 3266: 3263: 3260: 3240: 3237: 3234: 3231: 3225: 3222: 3216: 3213: 3210: 3207: 3204: 3198: 3195: 3189: 3186: 3183: 3180: 3177: 3174: 3170: 3167: 3164: 3161: 3158: 3152: 3149: 3143: 3137: 3134: 3128: 3125: 3105: 3074: 3071: 3068: 3062: 3059: 3053: 3047: 3044: 3038: 3035: 3015: 3012: 3006: 3003: 2997: 2991: 2988: 2965: 2962: 2959: 2956: 2950: 2947: 2941: 2935: 2932: 2926: 2923: 2900: 2897: 2891: 2885: 2882: 2859: 2853: 2850: 2844: 2838: 2835: 2829: 2826: 2823: 2817: 2814: 2808: 2802: 2799: 2793: 2790: 2767: 2764: 2738: 2735: 2704: 2701: 2681: 2678: 2653: 2650: 2648: 2645: 2633: 2629: 2626: 2621: 2615: 2610: 2607: 2584: 2580: 2576: 2556: 2536: 2512: 2492: 2468: 2464: 2459: 2455: 2452: 2449: 2446: 2443: 2440: 2420: 2400: 2380: 2360: 2340: 2320: 2275: 2270: 2247: 2242: 2239: 2236: 2231: 2227: 2223: 2218: 2214: 2210: 2207: 2204: 2199: 2195: 2191: 2186: 2182: 2178: 2175: 2172: 2167: 2163: 2159: 2154: 2150: 2146: 2143: 2140: 2135: 2131: 2127: 2122: 2118: 2114: 2094: 2087: 2083: 2078: 2075: 2072: 2067: 2063: 2059: 2054: 2050: 2046: 2043: 2037: 2033: 2028: 2025: 2020: 2016: 2012: 2007: 2003: 1999: 1996: 1990: 1986: 1981: 1978: 1973: 1969: 1965: 1960: 1956: 1952: 1949: 1943: 1939: 1934: 1931: 1926: 1922: 1918: 1913: 1909: 1905: 1881: 1875: 1868: 1864: 1860: 1855: 1851: 1844: 1839: 1835: 1828: 1822: 1815: 1811: 1807: 1802: 1798: 1791: 1788: 1783: 1779: 1758: 1753: 1747: 1744: 1742: 1739: 1738: 1735: 1732: 1730: 1727: 1726: 1724: 1719: 1714: 1710: 1706: 1701: 1697: 1690: 1685: 1681: 1677: 1672: 1668: 1645: 1641: 1618: 1614: 1589: 1584: 1578: 1575: 1572: 1570: 1567: 1566: 1563: 1560: 1558: 1555: 1554: 1552: 1547: 1542: 1538: 1526:Pauli matrices 1513: 1510: 1506: 1485: 1482: 1478: 1457: 1451: 1446: 1443: 1439: 1435: 1432: 1429: 1425: 1421: 1418: 1415: 1411: 1407: 1404: 1401: 1397: 1390: 1387: 1384: 1380: 1339: 1335: 1314: 1309: 1305: 1301: 1296: 1292: 1288: 1283: 1279: 1254: 1250: 1247: 1243: 1239: 1234: 1230: 1224: 1220: 1216: 1213: 1210: 1205: 1201: 1195: 1191: 1187: 1184: 1181: 1176: 1172: 1166: 1162: 1158: 1155: 1152: 1147: 1143: 1137: 1133: 1129: 1125: 1097: 1093: 1087: 1083: 1079: 1074: 1070: 1064: 1060: 1056: 1051: 1047: 1041: 1037: 1033: 1028: 1024: 1018: 1014: 993: 990: 970: 967: 962: 958: 954: 949: 945: 941: 936: 932: 928: 906: 902: 898: 893: 889: 885: 880: 876: 872: 850: 846: 842: 839: 834: 830: 807: 803: 799: 794: 790: 780:, then either 769: 766: 744: 740: 717: 713: 692: 686: 682: 678: 673: 669: 665: 660: 656: 652: 649: 644: 640: 636: 631: 627: 623: 618: 614: 610: 607: 602: 598: 592: 588: 584: 579: 575: 569: 565: 561: 556: 552: 546: 542: 538: 533: 529: 523: 519: 496: 492: 471: 468: 448: 445: 423: 419: 393: 389: 366: 362: 339: 335: 314: 311: 291: 288: 266: 262: 235: 231: 208: 204: 181: 177: 154: 150: 128: 125: 66:speed of light 38:Bell's theorem 26: 9: 6: 4: 3: 2: 13691: 13680: 13677: 13675: 13672: 13670: 13667: 13665: 13662: 13660: 13657: 13655: 13652: 13650: 13647: 13646: 13644: 13629: 13621: 13619: 13611: 13610: 13607: 13601: 13598: 13596: 13593: 13591: 13588: 13586: 13583: 13581: 13577: 13574: 13572: 13568: 13564: 13561: 13560: 13558: 13556: 13550: 13540: 13537: 13535: 13532: 13530: 13527: 13525: 13522: 13521: 13519: 13517: 13513: 13507: 13504: 13502: 13499: 13497: 13496:Spin qubit QC 13494: 13492: 13489: 13488: 13486: 13483: 13479: 13473: 13470: 13468: 13465: 13464: 13462: 13460: 13456: 13450: 13447: 13445: 13442: 13440: 13437: 13435: 13432: 13431: 13429: 13427: 13423: 13420: 13414: 13408: 13405: 13401: 13400: 13396: 13394: 13391: 13389: 13386: 13384: 13381: 13379: 13376: 13374: 13371: 13369: 13366: 13364: 13361: 13360: 13358: 13357: 13355: 13353: 13347: 13341: 13338: 13336: 13333: 13329: 13326: 13325: 13324: 13321: 13317: 13314: 13313: 13312: 13309: 13305: 13304:cluster state 13302: 13301: 13300: 13297: 13295: 13292: 13290: 13287: 13286: 13284: 13282: 13276: 13268: 13264: 13260: 13258: 13254: 13250: 13249: 13248: 13245: 13241: 13238: 13237: 13236: 13233: 13231: 13228: 13226: 13223: 13222: 13220: 13214: 13208: 13205: 13203: 13200: 13198: 13195: 13193: 13190: 13188: 13185: 13184: 13182: 13180: 13174: 13168: 13165: 13163: 13160: 13158: 13155: 13153: 13150: 13148: 13145: 13143: 13140: 13138: 13135: 13133: 13130: 13128: 13125: 13123: 13120: 13118: 13115: 13113: 13112:Deutsch–Jozsa 13110: 13108: 13105: 13103: 13100: 13098: 13095: 13094: 13092: 13090: 13086: 13076: 13073: 13069: 13066: 13064: 13061: 13059: 13056: 13055: 13054: 13051: 13049: 13048:Quantum money 13046: 13044: 13041: 13039: 13036: 13035: 13033: 13031: 13027: 13021: 13018: 13014: 13011: 13010: 13009: 13006: 13002: 12999: 12998: 12997: 12994: 12992: 12989: 12987: 12984: 12982: 12979: 12975: 12972: 12970: 12967: 12966: 12965: 12962: 12961: 12959: 12957:communication 12953: 12947: 12944: 12942: 12939: 12937: 12934: 12932: 12929: 12927: 12924: 12922: 12919: 12917: 12914: 12912: 12909: 12907: 12904: 12902: 12899: 12897: 12894: 12892: 12889: 12887: 12884: 12882: 12879: 12877: 12874: 12872: 12869: 12868: 12866: 12862: 12854: 12851: 12850: 12849: 12846: 12842: 12839: 12838: 12837: 12834: 12832: 12829: 12827: 12824: 12822: 12819: 12815: 12812: 12811: 12810: 12807: 12805: 12802: 12800: 12797: 12796: 12794: 12790: 12786: 12779: 12774: 12772: 12767: 12765: 12760: 12759: 12756: 12744: 12736: 12735: 12732: 12726: 12723: 12721: 12718: 12716: 12713: 12709: 12706: 12705: 12704: 12701: 12700: 12698: 12694: 12688: 12685: 12683: 12680: 12676: 12673: 12672: 12671: 12668: 12666: 12663: 12661: 12658: 12656: 12653: 12652: 12650: 12646: 12640: 12637: 12635: 12632: 12630: 12627: 12625: 12622: 12620: 12617: 12615: 12612: 12610: 12607: 12605: 12602: 12600: 12597: 12595: 12592: 12590: 12587: 12585: 12582: 12580: 12579:Quantum logic 12577: 12575: 12572: 12570: 12567: 12565: 12562: 12560: 12557: 12555: 12552: 12550: 12547: 12545: 12542: 12538: 12535: 12534: 12533: 12530: 12528: 12525: 12523: 12520: 12518: 12515: 12511: 12508: 12507: 12506: 12503: 12501: 12498: 12496: 12493: 12491: 12488: 12487: 12485: 12483: 12479: 12473: 12470: 12468: 12465: 12463: 12460: 12458: 12455: 12453: 12450: 12448: 12445: 12443: 12440: 12438: 12435: 12433: 12432:Quantum chaos 12430: 12428: 12425: 12423: 12420: 12419: 12417: 12415: 12411: 12405: 12402: 12400: 12399:Stern–Gerlach 12397: 12395: 12392: 12390: 12387: 12385: 12382: 12380: 12377: 12375: 12372: 12370: 12367: 12365: 12362: 12360: 12357: 12355: 12352: 12351: 12349: 12345: 12339: 12336: 12334: 12333:Transactional 12331: 12329: 12326: 12324: 12323:Quantum logic 12321: 12319: 12316: 12314: 12311: 12305: 12302: 12301: 12300: 12297: 12296: 12295: 12292: 12290: 12287: 12285: 12282: 12280: 12277: 12275: 12272: 12270: 12267: 12266: 12264: 12262: 12258: 12252: 12249: 12247: 12244: 12242: 12239: 12237: 12234: 12232: 12229: 12227: 12224: 12222: 12219: 12217: 12214: 12213: 12211: 12207: 12201: 12198: 12196: 12193: 12191: 12188: 12186: 12183: 12181: 12178: 12176: 12173: 12171: 12168: 12167: 12165: 12161: 12153: 12150: 12148: 12145: 12144: 12143: 12142:Wave function 12140: 12138: 12135: 12133: 12130: 12128: 12125: 12123: 12120: 12118: 12117:Superposition 12115: 12113: 12112:Quantum state 12110: 12108: 12105: 12103: 12100: 12098: 12095: 12093: 12090: 12088: 12085: 12083: 12080: 12076: 12073: 12071: 12068: 12066: 12065:Excited state 12063: 12061: 12058: 12057: 12056: 12053: 12051: 12048: 12046: 12043: 12041: 12038: 12036: 12033: 12032: 12030: 12026: 12020: 12017: 12015: 12012: 12010: 12007: 12003: 12000: 11999: 11998: 11995: 11993: 11990: 11989: 11987: 11983: 11979: 11972: 11967: 11965: 11960: 11958: 11953: 11952: 11949: 11941: 11937: 11936: 11931: 11927: 11923: 11922: 11917: 11913: 11910: 11907: 11906: 11895: 11891: 11887: 11881: 11877: 11873: 11869: 11865: 11861: 11857: 11853: 11849: 11845: 11840: 11836: 11830: 11826: 11825: 11820: 11816: 11812: 11808: 11804: 11800: 11796: 11792: 11788: 11784: 11779: 11774: 11770: 11766: 11761: 11757: 11753: 11749: 11745: 11741: 11737: 11733: 11729: 11725: 11721: 11716: 11712: 11708: 11704: 11698: 11694: 11689: 11684: 11679: 11675: 11671: 11667: 11663: 11662: 11657: 11652: 11648: 11643: 11632: 11628: 11624: 11619: 11618:1969.1/126533 11614: 11610: 11606: 11602: 11598: 11594: 11590: 11583: 11578: 11564: 11560: 11556: 11552: 11548: 11544: 11540: 11533: 11528: 11524: 11519: 11515: 11511: 11507: 11503: 11499: 11495: 11491: 11487: 11483: 11477: 11472: 11467: 11463: 11459: 11455: 11451: 11447: 11442: 11437: 11432: 11428: 11424: 11420: 11416: 11412: 11408: 11404: 11403: 11401: 11394: 11390: 11386: 11382: 11378: 11374: 11373:Physics Today 11369: 11365: 11361: 11357: 11353: 11349: 11345: 11341: 11337: 11333: 11329: 11325: 11323:0-375-72720-5 11319: 11315: 11314: 11309: 11308:Greene, Brian 11305: 11301: 11296: 11292: 11288: 11284: 11280: 11275: 11271: 11267: 11263: 11262: 11261: 11239: 11235: 11231: 11227: 11223: 11219: 11213: 11209: 11205: 11201: 11200: 11195: 11189: 11174: 11170: 11166: 11162: 11158: 11154: 11150: 11145: 11140: 11136: 11132: 11131: 11126: 11119: 11111: 11107: 11103: 11099: 11095: 11091: 11087: 11083: 11078: 11073: 11069: 11065: 11064: 11056: 11048: 11044: 11040: 11036: 11032: 11028: 11024: 11020: 11015: 11010: 11007:(3): 033002. 11006: 11002: 11001: 10996: 10992: 10985: 10976: 10971: 10967: 10960: 10942: 10938: 10932: 10928: 10924: 10919: 10914: 10907: 10906: 10898: 10890: 10886: 10882: 10878: 10874: 10870: 10865: 10860: 10856: 10852: 10851: 10846: 10842: 10836: 10828: 10824: 10820: 10818:9781316219393 10814: 10810: 10806: 10801: 10796: 10792: 10788: 10782: 10780: 10764: 10760: 10759: 10754: 10747: 10739: 10735: 10731: 10727: 10723: 10719: 10715: 10711: 10706: 10701: 10697: 10693: 10692: 10687: 10681: 10673: 10669: 10665: 10661: 10656: 10651: 10647: 10643: 10642: 10637: 10636:Mermin, N. D. 10631: 10623: 10621:0-691-08241-3 10617: 10613: 10609: 10603: 10595: 10591: 10587: 10581: 10577: 10573: 10567: 10559: 10555: 10551: 10545: 10541: 10537: 10532: 10527: 10523: 10516: 10508: 10504: 10500: 10496: 10492: 10488: 10484: 10480: 10476: 10472: 10471: 10463: 10455: 10451: 10447: 10443: 10439: 10435: 10430: 10425: 10421: 10417: 10413: 10406: 10392: 10388: 10381: 10372: 10367: 10363: 10359: 10355: 10351: 10350: 10345: 10338: 10330: 10326: 10322: 10318: 10314: 10310: 10306: 10302: 10297: 10292: 10288: 10284: 10283: 10275: 10267: 10263: 10258: 10253: 10249: 10245: 10241: 10237: 10232: 10227: 10223: 10219: 10218: 10213: 10206: 10198: 10194: 10190: 10186: 10182: 10178: 10174: 10170: 10165: 10160: 10156: 10152: 10151: 10143: 10128: 10127: 10122: 10115: 10107: 10103: 10099: 10095: 10090: 10085: 10081: 10077: 10073: 10069: 10068: 10063: 10056: 10048: 10044: 10040: 10036: 10032: 10028: 10024: 10020: 10015: 10010: 10006: 10002: 10001: 9993: 9985: 9981: 9977: 9973: 9969: 9965: 9960: 9955: 9951: 9947: 9940: 9938: 9929: 9925: 9921: 9917: 9913: 9909: 9904: 9899: 9895: 9891: 9890: 9882: 9874: 9870: 9866: 9862: 9858: 9854: 9850: 9846: 9842: 9838: 9837: 9829: 9820: 9815: 9811: 9807: 9803: 9799: 9798: 9793: 9786: 9775: 9774: 9766: 9758: 9754: 9750: 9746: 9742: 9738: 9737: 9729: 9725: 9721: 9715: 9701: 9700: 9695: 9691: 9690:Kaiser, David 9685: 9677: 9673: 9669: 9665: 9661: 9657: 9653: 9649: 9642: 9640: 9631: 9625: 9621: 9620: 9612: 9604: 9600: 9596: 9592: 9588: 9584: 9580: 9576: 9575: 9570: 9566: 9560: 9552: 9548: 9544: 9540: 9539: 9534: 9528: 9520: 9516: 9512: 9508: 9504: 9500: 9495: 9490: 9486: 9482: 9481: 9473: 9470:(July 1993). 9469: 9463: 9461: 9459: 9450: 9449: 9444: 9437: 9429: 9425: 9424: 9416: 9413: 9407: 9399: 9395: 9390: 9385: 9381: 9377: 9376: 9371: 9367: 9361: 9353: 9349: 9345: 9341: 9337: 9333: 9332: 9327: 9321: 9313: 9309: 9305: 9301: 9297: 9293: 9292: 9287: 9281: 9273: 9269: 9265: 9259: 9255: 9251: 9245: 9237: 9233: 9229: 9225: 9221: 9217: 9212: 9207: 9203: 9199: 9198: 9190: 9182: 9178: 9174: 9170: 9166: 9162: 9158: 9152: 9144: 9140: 9136: 9134:3-540-42756-2 9130: 9126: 9122: 9118: 9114: 9113:Kochen, Simon 9110: 9104: 9096: 9090: 9086: 9082: 9078: 9071: 9069: 9050: 9046: 9042: 9038: 9034: 9029: 9024: 9020: 9016: 9012: 9008: 9001: 8994: 8986: 8982: 8978: 8974: 8970: 8966: 8961: 8956: 8952: 8948: 8947: 8942: 8936: 8928: 8926:0-471-43958-4 8922: 8918: 8914: 8908: 8906: 8897: 8893: 8889: 8885: 8879: 8871: 8867: 8863: 8859: 8854: 8849: 8845: 8841: 8836: 8831: 8828:(7): 073035. 8827: 8823: 8822: 8817: 8810: 8802: 8798: 8794: 8790: 8786: 8782: 8778: 8774: 8769: 8764: 8761:(3): 032110. 8760: 8756: 8755: 8750: 8744: 8736: 8732: 8728: 8724: 8720: 8716: 8712: 8708: 8704: 8700: 8699: 8691: 8684:(2): 226–232. 8683: 8679: 8678: 8670: 8666: 8665:Kochen, Simon 8662: 8656: 8642: 8641: 8640:Plus Magazine 8636: 8629: 8615: 8614: 8609: 8602: 8594: 8590: 8586: 8582: 8578: 8574: 8569: 8564: 8560: 8556: 8555: 8550: 8549:Kochen, Simon 8546: 8540: 8532: 8528: 8524: 8520: 8516: 8512: 8508: 8504: 8499: 8494: 8490: 8486: 8485: 8477: 8469: 8465: 8461: 8457: 8453: 8449: 8445: 8441: 8437: 8433: 8432: 8427: 8421: 8413: 8409: 8405: 8401: 8397: 8393: 8389: 8385: 8384: 8376: 8368: 8364: 8360: 8356: 8352: 8348: 8344: 8340: 8336: 8332: 8331: 8326: 8319: 8312: 8308: 8304: 8300: 8296: 8292: 8288: 8284: 8280: 8279: 8274: 8273:Brown, Harvey 8270: 8264: 8256: 8252: 8248: 8246:0-7923-2549-4 8242: 8238: 8234: 8233: 8228: 8222: 8212: 8207: 8203: 8196: 8190: 8186: 8182: 8178: 8177:Weyl, Hermann 8172: 8164: 8160: 8159: 8151: 8147: 8141: 8133: 8129: 8125: 8119: 8115: 8111: 8107: 8103: 8097: 8089: 8088: 8083: 8077: 8069: 8065: 8061: 8057: 8052: 8047: 8043: 8039: 8035: 8031: 8025: 8017: 8013: 8009: 8005: 8001: 7997: 7996: 7991: 7985: 7976: 7971: 7967: 7963: 7959: 7955: 7954: 7949: 7945: 7944:Zeilinger, A. 7941: 7937: 7933: 7927: 7918: 7913: 7909: 7905: 7901: 7897: 7896: 7891: 7887: 7883: 7879: 7873: 7865: 7861: 7857: 7855:0-13-111892-7 7851: 7847: 7846: 7841: 7835: 7827: 7823: 7819: 7815: 7814: 7806: 7802: 7796: 7788: 7784: 7780: 7776: 7772: 7768: 7764: 7760: 7756: 7752: 7747: 7742: 7738: 7734: 7733: 7725: 7717: 7713: 7709: 7705: 7701: 7699:0-7695-2120-7 7695: 7691: 7687: 7683: 7679: 7674: 7669: 7665: 7661: 7657: 7653: 7647: 7639: 7635: 7631: 7625: 7621: 7620: 7612: 7604: 7600: 7596: 7592: 7588: 7584: 7583: 7578: 7571: 7563: 7559: 7555: 7551: 7547: 7543: 7539: 7535: 7534: 7529: 7522: 7514: 7510: 7506: 7500: 7496: 7495: 7490: 7486: 7480: 7478: 7476: 7474: 7465: 7464: 7459: 7455: 7451: 7445: 7443: 7428: 7427: 7422: 7418: 7412: 7404: 7400: 7396: 7392: 7388: 7384: 7380: 7376: 7371: 7366: 7362: 7358: 7357: 7349: 7333: 7329: 7328: 7323: 7317: 7309: 7305: 7301: 7299:9780521368698 7295: 7291: 7287: 7286:Bell, John S. 7281: 7277: 7263: 7258: 7251: 7247: 7231: 7208: 7205: 7202: 7199: 7190: 7170: 7150: 7130: 7110: 7102: 7098: 7094: 7093:deterministic 7088: 7079: 7058: 7054: 7030: 7025: 7021: 7012: 6986: 6959: 6946: 6938: 6910: 6902: 6898: 6894: 6866: 6847: 6834: 6830: 6826: 6825:David Hilbert 6822: 6816: 6806: 6802: 6791: 6788: 6786: 6783: 6781: 6778: 6776: 6773: 6771: 6768: 6766: 6763: 6761: 6758: 6756: 6753: 6751: 6748: 6746: 6745: 6741: 6739: 6736: 6735: 6730: 6724: 6719: 6712: 6710: 6705: 6703: 6699: 6692: 6682: 6680: 6675: 6672: 6668: 6657: 6653: 6651: 6647: 6643: 6633: 6631: 6627: 6622: 6619: 6615: 6611: 6607: 6598: 6593: 6583: 6581: 6577: 6572: 6569: 6563: 6561: 6556: 6552: 6547: 6545: 6539: 6536: 6532: 6528: 6524: 6520: 6516: 6510: 6500: 6496: 6487: 6483: 6481: 6480: 6475: 6471: 6461: 6458: 6454: 6453:Tsung-Dao Lee 6450: 6448: 6443: 6439: 6434: 6433:George Mackey 6429: 6427: 6423: 6418: 6416: 6412: 6407: 6403: 6395: 6391: 6387: 6383: 6379: 6375: 6371: 6367: 6363: 6359: 6355: 6351: 6347: 6343: 6342: 6341: 6338: 6336: 6335:Ernst Specker 6332: 6328: 6327:Grete Hermann 6324: 6320: 6316: 6310: 6306: 6291: 6289: 6284: 6281:introduced a 6280: 6264: 6256: 6252: 6248: 6243: 6239: 6230: 6227: 6223: 6216: 6213: 6210: 6204: 6199: 6196: 6192: 6183: 6180:of symmetric 6179: 6175: 6174:Werner states 6171: 6164: 6160: 6150: 6148: 6144: 6140: 6136: 6132: 6127: 6112: 6101: 6091: 6077: 6069: 6065: 6061: 6057: 6041: 6021: 6001: 5993: 5992:Hilbert space 5987: 5977: 5975: 5959: 5956: 5953: 5950: 5947: 5944: 5941: 5938: 5935: 5932: 5929: 5909: 5906: 5903: 5900: 5897: 5894: 5891: 5871: 5868: 5865: 5862: 5859: 5839: 5836: 5833: 5830: 5827: 5807: 5804: 5801: 5798: 5795: 5792: 5789: 5769: 5766: 5763: 5760: 5757: 5748: 5734: 5731: 5709: 5705: 5701: 5696: 5692: 5688: 5683: 5679: 5655: 5630: 5627: 5607: 5603: 5600: 5597: 5592: 5588: 5582: 5578: 5572: 5568: 5547: 5544: 5524: 5504: 5501: 5481: 5478: 5458: 5452: 5448: 5442: 5438: 5432: 5428: 5424: 5419: 5414: 5410: 5404: 5399: 5395: 5389: 5384: 5380: 5374: 5370: 5364: 5360: 5354: 5350: 5346: 5338: 5334: 5328: 5324: 5318: 5314: 5302: 5298: 5292: 5288: 5282: 5278: 5266: 5262: 5256: 5252: 5246: 5242: 5216: 5212: 5206: 5202: 5196: 5192: 5169: 5165: 5155: 5139: 5135: 5112: 5108: 5087: 5084: 5064: 5061: 5041: 5032: 5028: 5024: 5019: 5015: 5011: 5006: 5002: 4998: 4993: 4989: 4985: 4980: 4976: 4972: 4967: 4963: 4937: 4933: 4910: 4906: 4882: 4878: 4855: 4851: 4828: 4824: 4801: 4797: 4774: 4770: 4766: 4761: 4757: 4753: 4748: 4744: 4721: 4717: 4713: 4708: 4704: 4700: 4695: 4691: 4670: 4667: 4645: 4641: 4637: 4632: 4628: 4624: 4619: 4615: 4591: 4566: 4563: 4541: 4537: 4514: 4510: 4486: 4461: 4458: 4438: 4435: 4413: 4409: 4386: 4382: 4359: 4355: 4331: 4303: 4278: 4268: 4260: 4254: 4240: 4236: 4231: 4225: 4212: 4208: 4204: 4200: 4195: 4185: 4181: 4167: 4158: 4129: 4100: 4077: 4072: 4068: 4062: 4059: 4056: 4051: 4047: 4024: 4019: 4015: 4009: 4006: 3994: 3988: 3979: 3970: 3967: 3955: 3949: 3940: 3931: 3911: 3908: 3905: 3893: 3887: 3878: 3869: 3843: 3814: 3785: 3762: 3750: 3744: 3735: 3726: 3723: 3720: 3717: 3700: 3694: 3685: 3676: 3673: 3661: 3655: 3646: 3637: 3606: 3577: 3566: 3544: 3521: 3495: 3472: 3452: 3449: 3446: 3440: 3437: 3428: 3419: 3415: 3412: 3409: 3406: 3400: 3397: 3388: 3379: 3356: 3353: 3344: 3335: 3312: 3309: 3300: 3291: 3283: 3264: 3258: 3238: 3232: 3229: 3220: 3211: 3205: 3202: 3193: 3184: 3178: 3172: 3168: 3165: 3162: 3159: 3147: 3141: 3132: 3123: 3103: 3094: 3092: 3088: 3072: 3069: 3057: 3051: 3042: 3033: 3013: 3010: 3001: 2995: 2986: 2963: 2960: 2957: 2945: 2939: 2930: 2921: 2895: 2889: 2880: 2857: 2848: 2842: 2833: 2827: 2824: 2812: 2806: 2797: 2788: 2762: 2733: 2722: 2718: 2702: 2699: 2679: 2676: 2668: 2664: 2660: 2644: 2631: 2627: 2624: 2619: 2613: 2608: 2605: 2582: 2578: 2574: 2554: 2534: 2526: 2510: 2490: 2482: 2466: 2462: 2457: 2453: 2450: 2447: 2444: 2441: 2438: 2418: 2398: 2378: 2358: 2338: 2318: 2310: 2308: 2297: 2293: 2291: 2273: 2268: 2245: 2240: 2237: 2229: 2225: 2221: 2216: 2212: 2205: 2197: 2193: 2189: 2184: 2180: 2173: 2165: 2161: 2157: 2152: 2148: 2141: 2133: 2129: 2125: 2120: 2116: 2092: 2085: 2081: 2076: 2073: 2065: 2061: 2057: 2052: 2048: 2041: 2035: 2031: 2026: 2018: 2014: 2010: 2005: 2001: 1994: 1988: 1984: 1979: 1971: 1967: 1963: 1958: 1954: 1947: 1941: 1937: 1932: 1924: 1920: 1916: 1911: 1907: 1895: 1879: 1873: 1866: 1862: 1858: 1853: 1849: 1842: 1837: 1833: 1826: 1820: 1813: 1809: 1805: 1800: 1796: 1789: 1786: 1781: 1777: 1756: 1751: 1745: 1740: 1733: 1728: 1722: 1717: 1712: 1708: 1704: 1699: 1695: 1688: 1683: 1679: 1675: 1670: 1666: 1643: 1639: 1616: 1612: 1603: 1587: 1582: 1576: 1573: 1568: 1561: 1556: 1550: 1545: 1540: 1536: 1527: 1508: 1480: 1455: 1449: 1441: 1433: 1427: 1419: 1413: 1405: 1399: 1388: 1382: 1370: 1366: 1361: 1359: 1355: 1337: 1333: 1312: 1307: 1303: 1299: 1294: 1290: 1286: 1281: 1277: 1268: 1252: 1248: 1245: 1232: 1228: 1222: 1218: 1211: 1203: 1199: 1193: 1189: 1182: 1174: 1170: 1164: 1160: 1153: 1145: 1141: 1135: 1131: 1113: 1095: 1091: 1085: 1081: 1077: 1072: 1068: 1062: 1058: 1054: 1049: 1045: 1039: 1035: 1031: 1026: 1022: 1016: 1012: 991: 988: 968: 965: 960: 956: 947: 943: 939: 934: 930: 904: 900: 891: 887: 883: 878: 874: 848: 844: 840: 837: 832: 828: 805: 801: 797: 792: 788: 767: 764: 742: 738: 715: 711: 703:Because both 690: 684: 680: 671: 667: 663: 658: 654: 647: 642: 638: 629: 625: 621: 616: 612: 605: 600: 596: 590: 586: 582: 577: 573: 567: 563: 559: 554: 550: 544: 540: 536: 531: 527: 521: 517: 494: 490: 469: 466: 446: 443: 421: 417: 407: 391: 387: 364: 360: 337: 333: 312: 309: 289: 286: 264: 260: 251: 233: 229: 206: 202: 179: 175: 152: 148: 138: 137:Alice and Bob 133: 124: 122: 118: 113: 111: 110: 105: 101: 96: 94: 90: 86: 82: 77: 75: 71: 67: 63: 59: 55: 51: 47: 43: 39: 33: 19: 13669:Inequalities 13524:Charge qubit 13449:KLM protocol 13398: 13262: 13252: 12946:Purification 12876:Eastin–Knill 12870: 12462:Quantum mind 12374:Franck–Hertz 12216:Klein–Gordon 12170:Formulations 12163:Formulations 12092:Interference 12082:Entanglement 12060:Ground state 12055:Energy level 12028:Fundamentals 11992:Introduction 11933: 11919: 11875: 11847: 11843: 11823: 11768: 11764: 11723: 11719: 11692: 11668:(10): 8378. 11665: 11661:Scholarpedia 11659: 11646: 11635:. Retrieved 11592: 11589:Phys. Rev. A 11588: 11570:. Retrieved 11542: 11538: 11522: 11513: 11485: 11481: 11456:(2): 91–94. 11453: 11449: 11418: 11414: 11399: 11379:(4): 38–47. 11376: 11372: 11339: 11335: 11312: 11299: 11290: 11278: 11269: 11259: 11242:. Retrieved 11198: 11188: 11177:. Retrieved 11137:(2): 86–92. 11134: 11128: 11118: 11067: 11061: 11055: 11004: 10998: 10984: 10965: 10959: 10948:. Retrieved 10904: 10897: 10854: 10848: 10835: 10790: 10767:. Retrieved 10756: 10746: 10695: 10689: 10680: 10645: 10639: 10630: 10611: 10602: 10575: 10566: 10521: 10515: 10474: 10468: 10462: 10419: 10415: 10405: 10394:. Retrieved 10390: 10380: 10353: 10347: 10337: 10286: 10280: 10274: 10221: 10215: 10205: 10154: 10148: 10142: 10130:. Retrieved 10124: 10114: 10071: 10065: 10055: 10004: 9998: 9992: 9949: 9945: 9893: 9887: 9881: 9840: 9834: 9828: 9801: 9795: 9785: 9772: 9765: 9740: 9734: 9714: 9703:. Retrieved 9697: 9684: 9651: 9647: 9618: 9611: 9578: 9572: 9565:Peres, Asher 9559: 9545:(1): 25–45. 9542: 9536: 9527: 9484: 9478: 9447: 9436: 9427: 9421: 9406: 9379: 9373: 9360: 9335: 9329: 9320: 9295: 9289: 9280: 9253: 9244: 9201: 9195: 9189: 9164: 9160: 9151: 9124: 9109:Conway, John 9103: 9076: 9056:. Retrieved 9010: 9006: 8993: 8950: 8944: 8935: 8916: 8887: 8878: 8825: 8819: 8809: 8758: 8752: 8743: 8702: 8696: 8690: 8681: 8675: 8655: 8644:. Retrieved 8638: 8628: 8617:. Retrieved 8613:Science News 8611: 8601: 8561:(10): 1441. 8558: 8552: 8545:Conway, John 8539: 8488: 8482: 8476: 8435: 8429: 8426:Brown, H. R. 8420: 8387: 8381: 8375: 8334: 8328: 8318: 8310: 8282: 8276: 8263: 8231: 8227:Peres, Asher 8221: 8201: 8180: 8171: 8157: 8149: 8140: 8108:. Springer. 8105: 8096: 8086: 8076: 8041: 8037: 8024: 7999: 7993: 7984: 7960:(12): 1131. 7957: 7951: 7926: 7899: 7893: 7882:Podolsky, B. 7878:Einstein, A. 7872: 7844: 7834: 7817: 7811: 7795: 7736: 7730: 7724: 7659: 7646: 7618: 7611: 7589:(1): 22–56. 7586: 7580: 7570: 7537: 7531: 7521: 7493: 7461: 7430:. Retrieved 7424: 7411: 7360: 7354: 7348: 7336:. Retrieved 7325: 7316: 7289: 7280: 7262:E. T. Jaynes 7257: 7096: 7087: 7078: 6893:self-adjoint 6833:Hermann Weyl 6815: 6805: 6770:Mott problem 6742: 6706: 6701: 6694: 6676: 6663: 6654: 6639: 6623: 6614:Roland Omnès 6604: 6595: 6573: 6568:Alain Aspect 6564: 6554: 6550: 6548: 6540: 6531:Alain Aspect 6519:John Clauser 6514: 6512: 6498: 6484: 6477: 6473: 6470:page charges 6467: 6451: 6430: 6419: 6414: 6410: 6405: 6401: 6399: 6393: 6389: 6385: 6381: 6377: 6373: 6369: 6365: 6361: 6357: 6349: 6345: 6339: 6331:Simon Kochen 6312: 6166: 6163:Werner state 6135:Simon Kochen 6128: 6103: 6067: 6063: 6059: 6055: 5989: 5749: 5156: 4211:David Mermin 4197: 4182: 3564: 3095: 3090: 3086: 2655: 2306: 2302: 1602:measurements 1362: 1357: 1353: 1111: 408: 249: 134: 130: 117:philosophers 114: 107: 100:John Clauser 97: 88: 78: 37: 36: 13555:programming 13534:Phase qubit 13439:Circuit QED 12911:No-deleting 12853:cloud-based 12720:EPR paradox 12500:Quantum bus 12369:Double-slit 12347:Experiments 12313:Many-worlds 12251:Schrödinger 12200:Phase space 12190:Schrödinger 12180:Interaction 12137:Uncertainty 12107:Nonlocality 12102:Measurement 12097:Decoherence 12087:Hamiltonian 11510:Bell, J. S. 11316:. Vintage. 11287:Baggott, J. 10067:Nature News 9250:Bohm, David 8913:Jammer, Max 8209: [ 7940:Shimony, A. 7801:Bell, J. S. 7656:Watrous, J. 7327:Nobel Prize 7246:unit sphere 6810:experiment. 6775:PBR theorem 6490:Experiments 6305:EPR paradox 6147:Asher Peres 6131:John Conway 6060:guaranteed. 5100:, and each 2721:correlation 2652:Bell (1964) 2525:logical XOR 2481:logical AND 13643:Categories 13595:libquantum 13529:Flux qubit 13434:Cavity QED 13383:Bacon–Shor 13373:stabilizer 12901:No-cloning 12648:Extensions 12482:Technology 12328:Relational 12279:Copenhagen 12175:Heisenberg 12122:Tunnelling 11985:Background 11711:1180958776 11637:2018-03-19 11572:2009-03-18 11407:Aspect, A. 11244:2020-08-27 11179:2021-09-16 10950:2011-10-18 10800:1501.03521 10769:2021-09-16 10531:1501.05640 10396:2022-10-04 10296:1511.03190 10231:1511.03189 10164:1508.05949 10132:21 October 9705:2020-02-11 9494:1802.10119 9298:(1): 136. 9272:1103789975 9204:(2): 125. 9058:2017-10-28 8960:1805.10311 8835:1701.07801 8646:2022-04-23 8619:2022-04-23 8498:1909.11893 8484:Erkenntnis 7638:1256446911 7432:2020-02-08 7370:1805.04431 7272:References 6821:Paul Dirac 6422:David Bohm 6299:Background 6068:guaranteed 6064:impossible 6056:impossible 2659:David Bohm 1369:Bell state 279:is either 109:Bell tests 93:inequality 13501:NV center 12936:Threshold 12916:No-hiding 12881:Gleason's 12354:Bell test 12209:Equations 12035:Born rule 11940:EMS Press 11864:118769677 11778:0801.2184 11502:120840672 11364:122724592 11226:951761277 11144:0906.1626 11077:0704.2529 11047:118518558 11039:1367-2630 11014:1208.4119 10913:CiteSeerX 10827:118686956 10730:0034-6861 10705:0909.2359 10594:439453957 10572:Omnès, R. 10558:119214547 10507:122180759 10499:1751-8113 10429:1301.1069 10197:205246446 10014:1106.3224 9959:1407.0363 9603:0305-4470 9519:119546199 9286:Wu, C.-S. 9252:(1989) . 9211:0706.2661 9045:250885175 9023:CiteSeerX 8985:118951033 8896:872622725 8870:119428107 8862:1367-2630 8801:117284016 8793:1050-2947 8727:0556-2791 8531:202889160 8523:0165-0106 8468:122868901 8460:0015-9018 8412:122885859 8404:0031-8248 8367:120340929 8359:0015-9018 8299:0309-7013 8179:(1950) . 8132:463777694 7936:Horne, M. 7886:Rosen, N. 7771:0031-9007 7746:0910.3952 7652:Cleve, R. 7562:0031-9007 7513:844974180 7338:6 October 7250:connected 7232:ρ 7212:⟩ 7200:ρ 7197:⟨ 7194:→ 7111:− 7059:η 7034:⟩ 7031:ψ 7026:η 7013:ψ 7010:⟨ 6990:⟩ 6987:η 6950:⟩ 6947:ψ 6939:η 6936:⟨ 6911:η 6901:Born rule 6897:operators 6865:separable 6851:⟩ 6848:ψ 6698:free will 6551:detection 6523:Bell test 6509:Bell test 6420:In 1951, 6283:toy model 6277:In 2004, 6257:† 6249:⊗ 6244:† 6224:ρ 6214:⊗ 6193:ρ 6178:unitaries 6113:λ 6078:λ 6042:λ 6022:λ 6002:λ 5957:∨ 5951:∨ 5939:⊕ 5933:⊕ 5799:⊕ 5793:⊕ 5732:− 5706:σ 5702:⊗ 5693:σ 5689:⊗ 5680:σ 5659:⟩ 5656:ψ 5479:− 5166:σ 5136:σ 5109:σ 5062:− 4934:σ 4907:σ 4879:σ 4852:σ 4825:σ 4798:σ 4771:σ 4767:⊗ 4758:σ 4754:⊗ 4745:σ 4718:σ 4714:⊗ 4705:σ 4701:⊗ 4692:σ 4642:σ 4638:⊗ 4629:σ 4625:⊗ 4616:σ 4595:⟩ 4592:ψ 4538:σ 4511:σ 4490:⟩ 4487:ψ 4459:− 4410:σ 4383:σ 4356:σ 4335:⟩ 4307:⟩ 4272:⟩ 4261:− 4258:⟩ 4229:⟩ 4226:ψ 4162:→ 4133:→ 4104:→ 4063:− 4057:≰ 4010:− 3998:→ 3983:→ 3959:→ 3944:→ 3897:→ 3882:→ 3847:→ 3818:→ 3789:→ 3754:→ 3739:→ 3718:≤ 3704:→ 3689:→ 3674:− 3665:→ 3650:→ 3610:→ 3581:→ 3548:→ 3499:→ 3450:± 3441:λ 3432:→ 3410:± 3401:λ 3392:→ 3357:λ 3348:→ 3313:λ 3304:→ 3265:λ 3259:ρ 3233:λ 3224:→ 3206:λ 3197:→ 3179:λ 3173:ρ 3169:λ 3163:∫ 3151:→ 3136:→ 3104:λ 3061:→ 3046:→ 3005:→ 2996:⋅ 2990:→ 2961:− 2949:→ 2934:→ 2899:→ 2884:→ 2852:→ 2843:⋅ 2837:→ 2828:− 2816:→ 2801:→ 2766:→ 2737:→ 2700:− 2625:≈ 2235:⟩ 2222:⊗ 2209:⟨ 2206:− 2203:⟩ 2190:⊗ 2177:⟨ 2171:⟩ 2158:⊗ 2145:⟨ 2139:⟩ 2126:⊗ 2113:⟨ 2077:− 2071:⟩ 2058:⊗ 2045:⟨ 2024:⟩ 2011:⊗ 1998:⟨ 1977:⟩ 1964:⊗ 1951:⟨ 1930:⟩ 1917:⊗ 1904:⟨ 1894:Born rule 1863:σ 1859:− 1850:σ 1810:σ 1797:σ 1790:− 1709:σ 1680:σ 1640:σ 1613:σ 1574:− 1537:σ 1512:⟩ 1484:⟩ 1445:⟩ 1434:⊗ 1431:⟩ 1420:− 1417:⟩ 1406:⊗ 1403:⟩ 1386:⟩ 1383:ψ 1246:≤ 1238:⟩ 1215:⟨ 1212:− 1209:⟩ 1186:⟨ 1180:⟩ 1157:⟨ 1151:⟩ 1128:⟨ 1078:− 989:± 884:− 841:− 765:± 664:− 583:− 310:− 32:Bell test 13563:OpenQASM 13539:Transmon 13416:Physical 13216:Quantum 13117:Grover's 12891:Holevo's 12864:Theorems 12814:timeline 12804:NISQ era 12743:Category 12537:Timeline 12289:Ensemble 12269:Bayesian 12231:Majorana 12147:Collapse 12019:Glossary 12002:Timeline 11942:. 2001 . 11894:22906474 11874:(1991). 11811:11536757 11803:18518088 11756:11839894 11748:10054467 11631:Archived 11563:Archived 11310:(2004). 11289:(1992). 11268:(2001). 11238:Archived 11196:(2016). 11173:Archived 11169:16242184 11102:17443179 10941:Archived 10889:13998168 10763:Archived 10738:20551033 10610:(1979). 10574:(1994). 10454:55537196 10329:13789503 10321:26722905 10266:26722906 10189:26503041 10098:26333448 10047:16306493 10039:22107491 9984:40332044 9928:49487096 9865:10676953 9726:(1972). 9567:(1991). 9368:(1957). 9236:32755624 9143:49404213 9123:(eds.). 9049:Archived 8915:(1974). 8886:(1944). 8667:(2009). 8593:12999337 8255:28854083 8229:(1993). 8148:(1932). 8084:(1930). 7946:(1990). 7864:53926857 7842:(2005). 7803:(1964). 7787:17298392 7779:20481921 7708:55954993 7491:(2010). 7403:13665914 7395:29743691 7308:15053677 7288:(1987). 7046:, where 6974:, where 6715:See also 6555:locality 6288:monogamy 4529:and two 1358:locality 1115:averages 58:particle 13553:Quantum 13491:Kane QC 13350:Quantum 13278:Quantum 13207:PostBQP 13177:Quantum 13162:Simon's 12955:Quantum 12792:General 12696:Related 12675:History 12414:Science 12246:Rydberg 11997:History 11783:Bibcode 11728:Bibcode 11670:Bibcode 11627:9912775 11597:Bibcode 11547:Bibcode 11458:Bibcode 11423:Bibcode 11381:Bibcode 11344:Bibcode 11234:7779840 11149:Bibcode 11110:4412358 11082:Bibcode 11019:Bibcode 10869:Bibcode 10710:Bibcode 10660:Bibcode 10479:Bibcode 10434:Bibcode 10391:Reuters 10358:Bibcode 10356:: 123. 10349:Physics 10301:Bibcode 10257:5815856 10236:Bibcode 10169:Bibcode 10106:4409566 10076:Bibcode 10019:Bibcode 9964:Bibcode 9908:Bibcode 9873:4309261 9845:Bibcode 9806:Bibcode 9745:Bibcode 9676:1444158 9656:Bibcode 9583:Bibcode 9499:Bibcode 9398:0096113 9352:2308516 9300:Bibcode 9216:Bibcode 9169:Bibcode 9015:Bibcode 8965:Bibcode 8840:Bibcode 8773:Bibcode 8735:9902666 8707:Bibcode 8573:Bibcode 8503:Bibcode 8440:Bibcode 8339:Bibcode 8307:4106773 8215:. 1931. 8187:Dover. 8056:Bibcode 8004:Bibcode 7962:Bibcode 7904:Bibcode 7751:Bibcode 7716:8077237 7678:Bibcode 7591:Bibcode 7542:Bibcode 7460:(ed.). 7375:Bibcode 6895:linear 6646:Everett 6474:Physics 6294:History 6143:qutrits 2523:is the 1354:realism 194:. 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