量子无信号关联和非局部博弈
Quantum no-signalling correlations and non-local games
摘要：
我们介绍和检查三个子类的家庭的量子无信号（QNS）的相关性段和冬季介绍：量子交换，量子和本地。我们正式的概念，一个普遍的TRO的块算子等距，定义一个操作系统，普遍的随机算子矩阵，并实现它作为一个商的矩阵代数。我们描述类的QNS相关的两个副本的通用操作系统的张量积的状态，并专门的相关类和它们的表示经典到量子相关。我们研究了各种量子版本的同步无信号相关性，并表明它们具有不变性的性质，为合适的状态集。我们引入量子非局部游戏作为非局部游戏的推广。我们定义了量子博弈合成的运算，并证明了属于某类的完美策略在通道合成下是封闭的。我们专注于图着色的情况下，我们展示量子版本的正交秩的图作为最佳输出尺寸的完美的经典量子策略的图着色游戏存在，以及非交换图同态，我们确定量子版本的非交换图同态引入Stahlke。
英文摘要：
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.
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