On Possibilistic Conditions to Contextuality and Nonlocality

TL;DR

This paper explores the relationship between possibilistic paradoxes and logical contextuality in quantum mechanics, demonstrating that certain possibilistic conditions are both necessary and sufficient for contextuality in key scenarios.

Contribution

It introduces the concept of possibilistic paradoxes and establishes their equivalence with logical contextuality in significant quantum scenarios.

Findings

Existence of possibilistic paradoxes equivalent to logical contextuality.

Possibilistic paradoxes are necessary and sufficient for contextuality.

Implications for understanding quantum nonlocality without inequalities.

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.