A classification of hidden-variable properties

Brandenburger, Adam; Yanofsky, Noson S.

doi:10.1088/1751-8113/41/42/425302

Cited by 36 publications

(70 citation statements)

References 36 publications

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“…The above alternative version of (2.3) is more similar to the "λ-independence" assumption as formulated in [17]. (A.1) is also a stronger assumption than (2.3): one can verify that (A.1) directly implies (2.3), but the converse does not hold.…”

Section: Appendixmentioning

confidence: 95%

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A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

Bierhorst

2014

Found Phys

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The Clauser-Horne-Shimony-Holt (CHSH) inequality is a constraint that local hidden variable theories must obey. Quantum Mechanics predicts a violation of this inequality in certain experimental settings. Treatments of this subject frequently make simplifying assumptions about the probability spaces available to a local hidden variable theory, such as assuming the state of the system is a discrete or absolutely continuous random variable, or assuming that repeated experimental trials are independent and identically distributed. In this paper, we do two things: first, show that the CHSH inequality holds even for completely general state variables in the measure-theoretic setting, and second, demonstrate how to drop the assumption of independence of subsequent trials while still being able to perform a hypothesis test that will distinguish Quantum Mechanics from local theories. The statistical strength of such a test is computed.

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Section: Appendixmentioning

confidence: 95%

“…This will allow us to directly compare our system to the system of [17], as well as to illustrate and clarify the nature of our particular choices of assumptions.…”

Section: Appendixmentioning

confidence: 99%

A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

Bierhorst

2014

Found Phys

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“…In the literature, this has received various names: measurement independence [8], λ-independence [25], free will [15] and no-conspiracy [6]. Complete independence of the measurement choices from any physical parameter influencing the measurement outputs, which is typically justified by an appeal to the experimentalist's free will [26], may seem too strong of an assumption and one may wonder what happens with the validity of Bell's theorem when this requirement is, somehow, relaxed.…”

Section: Randomness At the Inputsmentioning

confidence: 99%

Randomness and Non-Locality

2016

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The concepts of randomness and non-locality are intimately intertwined: outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.

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“…Hidden-variable (HV) theories endeavor to give a satisfactory representation of our intuition while reproducing the experimental predictions of quantum theory [2][3][4][5][6]. Imposing classical concepts (determinism, versions of locality, etc) on HV models constrains the resulting probability distributions.…”

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confidence: 99%

“…A HV theory is adequate [3,4,6] if it reproduces the experimentally observed statistics. Here we investigate not if a proposed HV theory is adequate (in a world described by quantum theory), but if any statistics with marginal distributions (5) and (7) can be based on it.…”

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confidence: 99%

Determinism, Independence, and Objectivity are Incompatible

2015

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*Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual compatibility of apparently reasonable classical assumptions. We analyse a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (the assertion that quantum systems are, at any moment, either particles or waves, but not both). These three ideas are incompatible with any theory, not only with quantum mechanics.Introduction. -Most of the quantum formalism was in place by 1932 [1]. Since then, quantum theory has been spectacularly successful across all the investigated scales and systems. Yet many of its results contradict both common sense and classical physical intuition. Wave-particle duality, superposition, and entanglement are among these counterintuitive features [2,3] and the "strictly instrumentalist" [4] core of quantum theory abandons many familiar traits of classical physics. As a result, there are profound differences of opinion on the meaning of quantum theory and the desire to explain or even to remove its puzzling properties [2][3][4][5].Hidden-variable (HV) theories endeavor to give a satisfactory representation of our intuition while reproducing the experimental predictions of quantum theory [2-6]. Imposing classical concepts (determinism, versions of locality, etc) on HV models constrains the resulting probability distributions. This may lead to "paradoxes," i.e., an incompatibility of the allegedly reasonable assumptions with the predictions of quantum theory.With the advent of quantum technologies [7,8] we can now realize classic gedankenexperiments and develop new tests to confront the predictions of HV theories with those of quantum mechanics. When the latter are experimentally confirmed, HV models fail the crucial test of adequacy and, unless some loophole for the experiment is found [9], should either be abandoned or amended to include deep, possibly unacceptable [5], conspiratorial correlations. The loopholes, in turn, may be countered by more sophisticated set-ups [10].Implicit in these debates is the premise that classically reasonable assumptions form a world view which, although experimentally inadequate, is nevertheless consistent. We question this tacit assumption and investigate the mutual compatibility of three classical requirements (determinism, independence, objectivity). Specifically, in the context of waveparticle duality and delayed-choice experiments [11,12] we inquire if it is possible to find any probability distribution that satisfies all three classical constraints. Here we answer this question in the negative: determinism, independence, and objectivity are incompatible; i.e., no such probability distribu-

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A classification of hidden-variable properties

Cited by 36 publications

References 36 publications

A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

Randomness and Non-Locality

Determinism, Independence, and Objectivity are Incompatible

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