On Possibilistic Conditions to Contextuality and Nonlocality

Abstract

Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and inequality-free proofs. The former can be understood as the possibility version of contextuality, while the latter refers to proofs of quantum contextuality/nonlocality that are not based on violations of some noncontextuality (or Bell) inequality. The present work aims to build a bridge between these two concepts from what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality/nonlocality. As main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios. Finally, we discuss some interesting consequences arising from the completeness of these possibilistic paradoxes.

arXiv commentTo appear in Phys. Rev. A. Comments still welcome!

References in corpus (30)

• Bell nonlocality
• No Signalling and Quantum Key Distribution
• Contextuality supplies the magic for quantum computation
• A simple test for hidden variables in spin-1 system
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• Bell-Kochen-Specker theorem: A proof with 18 vectors
• Contextuality in Measurement-based Quantum Computation
• All noncontextuality inequalities for the n-cycle scenario
• The contextual fraction as a measure of contextuality
• Wigner function negativity and contextuality in quantum computation on rebits
• Device-independent bounds for Hardy's experiment
• Entropic Test of Quantum Contextuality
• Simple Hardy-like proof of quantum contextuality
• Nonlocality of Symmetric States
• Hardy's nonlocality for generalized n-particle GHZ states
• Hardy's Paradox for High-Dimensional Systems: Beyond Hardy's Limit
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Experimental observation of Hardy-like quantum contextuality
• Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
• Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality
• General Hardy-Type Paradox Based on Bell inequality and its Experimental Test
• Hardy's paradox for multi-settings and high-dimensional systems
• Indistinguishability of causal relations from limited marginals
• Consequences and applications of the completeness of Hardy's nonlocality
• Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states
• Contextuality and bundle diagrams
• Contextuality under weak assumptions
• The Exclusivity Principle and the Set of Quantum Correlations
• On the computational complexity of detecting possibilistic locality
• Sheaf-Theoretic Methods in Quantum Mechanics and Quantum Information Theory

Cited by in corpus (5)

• A possibilistic no-go theorem on the Wigner's friend paradox
• Violating the KCBS inequality with a toy mechanism
• Extended Wigner's friend paradoxes do not require nonlocal correlations
• Connecting extended Wigner's friend arguments and noncontextuality
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications