论文标题
量子无信号相关性和非本地游戏
Quantum no-signalling correlations and non-local games
论文作者
论文摘要
我们介绍并检查了Duan和Winter引入的量子无标志性（QNS）相关性的三个子类：量子通勤，量子和局部。我们正式化了块操作员等轴测图的通用TRO的概念，定义了操作员系统，用于随机运算符矩阵的通用系统，并将其视为矩阵代数的商。我们描述了QNS相关性的类别，该类别是在通用运算符系统的两个副本的张量产品上的状态，并将相关类别及其表示为经典之间的相关性。我们研究了各种量子版本的同步无信号相关性，并表明它们具有适当状态集的不变特性。我们将量子非本地游戏引入非本地游戏的概括。我们定义了量子游戏组成的操作，并表明属于某个类别的完美策略是在频道组成下关闭的。我们专注于图形色素的情况，在该情况下，我们展示了图的正交等级的量子版本，这是最佳的输出维度，存在图形着色游戏的完美经典到量子策略，以及非交互性图同质性的非公认图形同质性，在那里我们在其中识别出非辅助图的量子版本。
We introduce and examine three subclasses of the family of quantum no-signalling (QNS) correlations introduced by Duan and Winter: quantum commuting, quantum and local. We formalise the notion of a universal TRO of a block operator isometry, define an operator system, universal for stochastic operator matrices, and realise it as a quotient of a matrix algebra. We describe the classes of QNS correlations in terms of states on the tensor products of two copies of the universal operator system, and specialise the correlation classes and their representations to classical-to-quantum correlations. We study various quantum versions of synchronous no-signalling correlations and show that they possess invariance properties for suitable sets of states. We introduce quantum non-local games as a generalisation of non-local games. We define the operation of quantum game composition and show that the perfect strategies belonging to a certain class are closed under channel composition. We specialise to the case of graph colourings, where we exhibit quantum versions of the orthogonal rank of a graph as the optimal output dimension for which perfect classical-to-quantum strategies of the graph colouring game exist, as well as to non-commutative graph homomorphisms, where we identify quantum versions of non-commutative graph homomorphisms introduced by Stahlke.
