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  • Letter
  • Open Access

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

Yuan Liu1, Ho Yiu Chung1, Emmanuel Zambrini Cruzeiro2, Junior R. Gonzales-Ureta3, Ravishankar Ramanathan1,*, and Adán Cabello4,5,†

  • *Contact author: ravi@cs.hku.hk
  • †Contact author: adan@us.es
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Phys. Rev. Research 6, L042035 – Published 4 November, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042035

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, because of the FNS = FN = AVN = PT equivalence, has implications in several fields.

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Phys. Rev. Research 6, L042035– Published 4 November, 2024
  • Received 20 October 2023
  • Accepted 16 October 2024
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