Characterization of Binary Constraint System Games
Abstract
We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary variables and m constraints. We show that, whenever there is a perfect entangled protocol for such a game, there exists a set of binary observables with commutations and products similar to those exhibited by Mermin. We also show how to derive upper bounds strictly below 1 for the the maximum entangled success probability of some BCS games. These results are partial progress towards a larger project to determine the computational complexity of deciding whether a given instance of a BCS game admits a perfect entangled strategy or not.
Cite
@article{arxiv.1209.2729,
title = {Characterization of Binary Constraint System Games},
author = {Richard Cleve and Rajat Mittal},
journal= {arXiv preprint arXiv:1209.2729},
year = {2013}
}
Comments
Revised version corrects an error in the previous version of the proof of Theorem 1 that arises in the case of POVM measurements