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arXiv · 2310.10600

Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy

Yuan Liu·Ho Yiu Chung·Emmanuel Zambrini Cruzeiro·Junior R. Gonzales-Ureta·Ravishankar Ramanathan·Adán Cabello
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Abstract

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, due to the FNS=FN=AVN=PT equivalence, has implications in several fields.

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Yuan Liu, Ho Yiu Chung, Emmanuel Zambrini Cruzeiro, Junior R. Gonzales-Ureta, Ravishankar Ramanathan, Adán Cabello. 2023-10-16. Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy. https://doi.org/10.1103/physrevresearch.6.l042035

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