2023/02/09 by Sizhuo Yan, Yan, Sizhuo, Jianting Yang +5 · 1 citation
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum Information and Cryptography #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.2302.04557
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 Gröbner basis computation and semidefinite programming is given for certifying that a given mirror game has no perfect commuting operator strategies.