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

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.

5+8 pages, 2+2 figures

References in corpus (29)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Quantum advantage with shallow circuits
• A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
• Graph-Theoretic Approach to Quantum Correlations
• Violation of Bell's inequality: criterion for quantum communication complexity advantage
• Bell Inequalities for Graph States
• Maximally Non-Local and Monogamous Quantum Correlations
• Full randomness from arbitrarily deterministic events
• Quantum Pseudo-Telepathy
• Geometry of the set of quantum correlations
• "All versus nothing" inseparability for two observers
• Improving zero-error classical communication with entanglement
• Bell's theorem without inequalities and without probabilities for two observers
• All-Versus-Nothing Violation of Local Realism by Two-Photon, Four-Dimensional Entanglement
• Lifting Bell inequalities
• "All-versus-nothing" nonlocality test of quantum mechanics by two-photon hyperentanglement
• All-Versus-Nothing Violation of Local Realism for Two Entangled Photons
• Fully nonlocal quantum correlations
• Playing Games with Multiple Access Channels
• Experimental fully contextual correlations
• Parallel Device-Independent Quantum Key Distribution
• Simple explanation of the quantum limits of genuine $n$-body nonlocality
• Quantum correlations from simple assumptions
• Bell Inequalities From No-Signalling Distributions
• Experimental Demonstration of Quantum Pseudotelepathy
• Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game
• No quantum realization of extremal no-signaling boxes
• Local Randomness: Examples and Application
• Tight Bell inequalities from polytope slices

Cited by in corpus (9)

• Simplest bipartite perfect quantum strategies
• The simplest Kochen-Specker set
• Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
• All genuinely entangled stabilizer subspaces are multipartite fully nonlocal
• Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
• How contextuality and antidistinguishability are related
• Supersinglets can be self-tested with perfect quantum strategies
• Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications