A Characterization of Perfect Strategies for Mirror Games
Operator Algebras
2023-05-12 v3 Quantum Physics
Abstract
We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization of whether or not a mirror game has perfect commuting operator strategies. This new characterization uses a smaller algebra introduced by Paulsen and others for synchronous games and the noncommutative Nullstellensatz developed by Cimpric, Helton and collaborators. An algorithm based on noncommutative Gr\"obner basis computation and semidefinite programming is given for certifying that a given mirror game has no perfect commuting operator strategies.
Keywords
Cite
@article{arxiv.2302.04557,
title = {A Characterization of Perfect Strategies for Mirror Games},
author = {Sizhuo Yan and Jianting Yang and Tianshi Yu and Lihong Zhi},
journal= {arXiv preprint arXiv:2302.04557},
year = {2023}
}
Comments
To appear ISSAC'2023 Proc. 2023 Internat. Symp. Symbolic Algebraic Comput