Characterization of Binary Constraint System Games

摘要

We investigate a simple class of multi-prover interactive proof systems (classical non-local games), called binary constraint system (BCS) games, and characterize those that admit a perfect entangled strategy (i.e., a strategy with value 1 when the provers can use shared entanglement). Our characterization is in terms of a system of matrix equations. One application of this characterization is that, combined with a recent result of Arkhipov, it leads to a simple algorithm for determining whether certain restricted BCS games have a perfect entangled strategy, and, for the instances that do not, for bounding their value strictly below 1. An open question is whether, for the case of general BCS games, making this determination is computationally decidable. Our characterization might play a useful role in the resolution of this question.