Classical, quantum and nonsignalling resources in bipartite games

• Published in: Theoretical computer science Vol. 486; pp. 61 - 72
• Main Authors: Brassard, Gilles, Broadbent, Anne, Hänggi, Esther, Méthot, André Allan, Wolf, Stefan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 20-05-2013
• Subjects: Bell theorems; Graph theory; Interactive proof systems; Nonlocality; Pseudotelepathy; Pseudotelepathy; Graph theory; Nonlocality; Bell theorems; Interactive proof systems
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2012.12.017

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.