Transitive Nonlocal Games
Quantum Physics
2024-12-10 v1 Combinatorics
Quantum Algebra
Abstract
We study a class of nonlocal games, called transitive games, for which the set of perfect strategies forms a semigroup. We establish several interesting correspondences of bisynchronous transitive games with the theory of compact quantum groups. In particular, we associate a quantum permutation group with each bisynchronous transitive game and vice versa. We prove that the existence of a C*-strategy, the existence of a quantum commuting strategy, and the existence of a classical strategy are all equivalent for bisynchronous transitive games. We then use some of these correspondences to establish necessary and sufficient conditions for some classes of correlations, that arise as perfect strategies of transitive games, to be nonlocal.
Keywords
Cite
@article{arxiv.2312.12040,
title = {Transitive Nonlocal Games},
author = {Prem Nigam Kar and Jitendra Prakash and David E Roberson},
journal= {arXiv preprint arXiv:2312.12040},
year = {2024}
}