A Characterization of Perfect Strategies for Mirror Games

Autor:	Yan, Sizhuo, Yang, Jianting, Yu, Tianshi, Zhi, Lihong
Rok vydání:	2023
Předmět:	Mathematics - Operator Algebras Quantum Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: To appear ISSAC'2023 Proc. 2023 Internat. Symp. Symbolic Algebraic Comput
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.04557 Zobrazit plný text záznamu View this record from Arxiv