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arXiv:quant-ph/0511123 · Physical Review A

Two-player quantum pseudotelepathy based on recent all-versus-nothing violations of local realism

Adán Cabello

Published Feb 1, 2006• 7 citations
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Abstract

We introduce two two-player quantum pseudotelepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell's theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and M\'ethot's claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light cone (quant-ph/0511047) is incorrect.

DOI
10.1103/physreva.73.022302

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We introduce two two-player quantum pseudotelepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell's theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and M'ethot's claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light cone (quant-ph/0511047) is incorrect.
We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408 (2003)] to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell inequality which resembles Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)] but requires only two observers.
We introduce an extended version of a previous all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom (A. Cabello, quant-ph/0507259), which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this extended version gives $\ensuremath{\eta}>0.69$. This efficiency is lower than that required for previous proposals.
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.
We show that a quantum correlation p is in a face of the nonsignaling polytope with no local points if and only if p has nonlocal content 1, if and only if p allows for a Greenberger-Horne-Zeilinger-like proof, and if and only if p provides a perfect strategy for a nonlocal game. That is, face nonsignaling (FNS) correlations, full nonlocality (FN), all-versus-nothing (AVN) proofs, and pseudotelepathy (PT) are equivalent. This shows that different resources behind a wide variety of fundamental results are in fact the same resource. We demonstrate that quantum correlations with FNS = FN = AVN = PT do not need to maximally violate a tight Bell inequality. We introduce a method for identifying quantum FNS = FN = AVN = PT correlations and use it to prove quantum mechanics does not allow for FNS = FN = AVN = PT neither in the ( 3 , 3 ; 3 , 2 ) nor in the ( 3 , 2 ; 3 , 4 ) Bell scenarios. This solves an open problem that, because of the FNS = FN = AVN = PT equivalence, has implications in several fields. Published by the American Physical Society 2024
There are different approaches to proving the impossibility of classical hidden-variable explanations of quantum-mechanical behavior. Whereas Kochen and Specker proved that a three-or higher-dimensional quantum-mechanical system cannot be "classically" prepared for all possible alternative measurements in a consistent way, Bell showed that the behavior of certain two-partite systems is nonlocal, i.e., inexplicable by shared classical information. We show a close connection between deterministic manifestations of such nonlocality-called "pseudotelepathy" games-and Kochen and Specker's theorem: Every such game leads to a Kochen-Specker contradiction, and vice versa