Synchronicity for quantum non-local games
Synchronicity for quantum non-local games
复制标题
DOI：
10.1016/j.jfa.2022.109738
复制
发表时间：
2021-06
影响因子：
1.7
通讯作者：
Michael Brannan;Samuel J. Harris;I. Todorov;L. Turowska
中科院分区：
文献类型：
--
作者：
Michael Brannan;Samuel J. Harris;I. Todorov;L. Turowska
我们引入了并发量子非局域博弈、量子输出镜像博弈和并发经典对量子非局域博弈作为同步非局域博弈的量子版本，并给出了它们在各种相关类中的完美策略的轨迹刻画。我们定义了并发经典-量子和并发量子非局部对策的*-代数和C*-代数，以及图的正交秩的代数形式。我们证明了量子图的量子同态可以看作是纠缠辅助的图的经典同态，并给出了量子图同态博弈的完美量子交换和完美近似量子策略的描述。我们将后一种结果专门用于游戏的输入基于经典图的情况。
We introduce concurrent quantum non-local games, quantum output mirror games and concurrent classical-to-quantum non-local games, as quantum versions of synchronous non-local games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes. We define *-algebras and C*-algebras of concurrent classical-to-quantum and concurrent quantum non-local games, and algebraic versions of the orthogonal rank of a graph. We show that quantum homomorphisms of quantum graphs can be viewed as entanglement assisted classical homomorphisms of the graphs, and give descriptions of the perfect quantum commuting and the perfect approximately quantum strategies for the quantum graph homomorphism game. We specialise the latter results to the case where the inputs of the game are based on a classical graph.