论文标题
量子公制空间的非本地游戏和量子对称性
Non-local games and quantum symmetries of quantum metric spaces
论文作者
论文摘要
在Kuperberg和Weaver的意义上，我们将Banica的量子等轴测图构造为量子公制空间的类别。我们还在两个量子公制空间之间引入量子异构体，我们表明，如果一对量子度量空间是代数量子等轴测图，则它们的量子等值组是单一的等效性。在最新的图形同构游戏上的动机中，我们引入了一个新的两人非本地游戏，称为公制等轴测游戏，当时且仅当指标空间是等轴测图时，玩家才能经典地获胜。赢得该游戏的量子策略与度量空间的量子等法一致。
We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we show that if a pair of quantum metric spaces are algebraically quantum isometric, then their quantum isometry groups are monoidally equivalent. Motivated by the recent work on the graph isomorphism game, we introduce a new two-player non-local game called the metric isometry game, where players can win classically if and only if the metric spaces are isometric. Winning quantum strategies of this game align with quantum isometries of the metric spaces.
