Quantum communication games manifest preparation contextuality

TL;DR

This paper establishes a fundamental link between performance in quantum communication games and the degree of preparation contextuality, providing a versatile framework for testing and understanding quantum contextuality.

Contribution

It introduces a general framework connecting communication game performance with preparation contextuality, enabling new tests and insights into quantum nonclassicality.

Findings

Quantum violations of Bell inequalities relate to preparation noncontextuality.

The framework reveals preparation contextuality of the maximally mixed state in any dimension.

Multiple examples of tests for preparation contextuality are derived.

Abstract

Communication games are collaborative information processing tasks involving a number of players with limited communication. Such games are useful tools for studying physical theories. A physical theory exhibits preparation contextuality whenever observed behaviour cannot be explained by a preparation noncontextual model. Here we show that there is a fundamental connection between the performance in communication games and the degree of preparation (non)contextuality. For this purpose, we present a general framework that allows us to construct communication games such that the game performance corresponds to a measure of preparation (non)contextuality. We illustrate the power of this framework by, 1) deriving many examples of tests of preparation contextuality, 2) showing that quantum violations of Bell inequalities can be derived from quantum violations of preparation noncontextuality, 3) qualitatively and quantitatively explaining related previous results on preparation contextuality in quantum communication games, and 4) solving the open problem of revealing the preparation contextuality of the maximally mixed quantum state in any dimension.