We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C ∗ ( G ) $C^{*}(\mathcal {G})$ to any imitation game G $\mathcal {G}$ , and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G $\mathcal {G}$ can be characterised in terms of properties of this C*-algebra. We single out a subclass of imitation games, which we call mirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra.

中文翻译：

---

非本地游戏的完美策略

我们根据算子系统张量积的状态描述了非信令二分相关的主要类别。这导致了另一类新游戏的引入，称为反射游戏，其特征是使用给定策略可以赢得的最难的非本地游戏。我们根据运营商系统商数提供了他们完美策略的特征。我们引入了一类新的非局部博弈，称为模仿博弈，其中玩家表现出关联的行为，其中包含变量分配博弈、二元约束系统博弈、同步博弈、许多基于图的博弈等类作为子类。独特的游戏。我们将 C*-代数 C ∗ ( G ) $C^{*}(\mathcal {G})$ 关联到任何模仿游戏 G $\mathcal {G}$ ，并证明 G$\mathcal {G}$ 的完美量子交换（分别是量子，局部）策略的存在可以根据这个 C*-代数的性质来表征。我们挑选出一个模仿游戏的子类，我们称之为镜像游戏，并提供了它们具有代数风味的量子交换策略的特征，此外还表明，它们的近似量子完美策略来自编码 C*-代数上的适用痕迹.