Characterising the Performance of XOR Games and the Shannon Capacity of Graphs

TL;DR

This paper establishes conditions under which quantum players do not outperform classical players in XOR games and links these conditions to the Shannon capacity of associated graphs, advancing understanding of quantum advantage in communication.

Contribution

It provides necessary and sufficient conditions for quantum advantage in XOR games and introduces a method to compute Shannon capacity for a broad class of graphs.

Findings

Identifies conditions where quantum and classical XOR game performances are equal.

Associates graphs with XOR games to analyze their zero-error communication capacity.

Defines new classes of graphs with computable Shannon capacity.

Abstract

In this paper we give a set of necessary and sufficient conditions such that quantum players of a two-party {\sc xor} game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrisation of new families of games which have no quantum advantage, for arbitrary input probability distributions up to certain symmetries. In the future, these might be used in information-theoretic studies on reproducing the set of quantum non-local correlations.