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

作者：Yuan Liu, Ho Yiu Chung, Emmanuel Zambrini Cruzeiro, Junior R. Gonzales-Ureta, Ravishankar Ramanathan, Adán Cabello · 发表于：Physical Review Research · 年份：2024 · DOI：10.1103/physrevresearch.6.l042035 · 被引用次数：11 · 研究领域：Quantum Mechanics and Applications、Philosophy and Theoretical Science、Computability, Logic, AI Algorithms

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