Classical, quantum and nonsignalling resources in bipartite games

Authors:
Gilles Brassard;Anne Broadbent;Esther Hänggi;André Allan Méthot;Stefan Wolf
Affiliations:
Département dinformatique et de recherche opérationnelle, Université de Montréal, CP 6128, Succursale centre-ville, Montréal (Québec), H3C 3J7 Canada;Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1 Canada;Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland;Group of Applied Physics, Université de Genève, Rue de lÉcole-de-Médecine 20, 1211 Genève 4, Switzerland;Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland and Faculty of Informatics, University of Lugano, 6900 Lugano, Switzerland
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

We study bipartite games that arise in the context of nonlocality with the help of graph theory. Our main results are alternate proofs that deciding whether a no-communication classical winning strategy exists for certain games (called forbidden-edge and covering games) is NP-complete, while the problem of deciding if these games admit a nonsignalling winning strategy is in P. We discuss relations between quantum winning strategies and orthogonality graphs. We also show that every pseudotelepathy game yields both a proof of the Bell-Kochen-Specker theorem and an instance of a two-prover interactive proof system that is classically sound, but that becomes unsound when provers use shared entanglement.