Revealing universal quantum contextuality through communication games

TL;DR

This paper extends logical proofs of quantum contextuality for qubits, derives inequalities to test non-contextuality, and introduces communication games that reveal quantum non-classicality even without non-locality.

Contribution

It generalizes contextuality proofs for qubits, derives testable inequalities, and proposes communication games to detect universal quantum contextuality under minimal assumptions.

Findings

Quantum theory violates universal non-contextual inequalities.

Communication games can reveal quantum contextuality without non-locality.

Universal quantum contextuality can be tested with minimal assumptions.

Abstract

A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.