title: Characterizing the performance of XOR games and the Shannon capacity of graphs.
abstract: In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party 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 parametrization of new families of games that 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 nonlocal correlations.
authors.affiliation: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and University of Gdańsk, 80-952 Gdańsk, Poland.
authors.forename: Ravishankar
authors.initials: R
authors.lastname: Ramanathan
authors.affiliation: Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom.
authors.forename: Alastair
authors.initials: A
authors.lastname: Kay
authors.affiliation: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil.
authors.forename: Gláucia
authors.initials: G
authors.lastname: Murta
authors.affiliation: National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland and Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233 Gdańsk, Poland.
authors.forename: Paweł
authors.initials: P
authors.lastname: Horodecki