论文标题
量子超晶型同态和非本地游戏
Quantum hypergraph homomorphisms and non-local games
论文作者
论文摘要
使用信息理论中的仿真范式，我们定义了量子超图同构和量子超图同构的概念，并表明它们分别构成了部分顺序和等效关系。我们专门针对非本地游戏产生的基础超图，我们定义了量子非本地游戏同构和量子非本地游戏同构的概念，并表明与给定相关类型相对于这种类型具有相等的值和渐近值的同构游戏。我们研究了一类新的无信号相关性，这些相关性见证了非本地游戏同态的存在，并以规范操作员系统的张量产品的状态来表征它们。我们定义了共同的同步相关性，并表明它们对应于与游戏派对相关的规范C* - 代数的张量产品的痕迹。
Using the simulation paradigm in information theory, we define notions of quantum hypergraph homomorphisms and quantum hypergraph isomorphisms, and show that they constitute partial orders and equivalence relations, respectively. Specialising to the case where the underlying hypergraphs arise from non-local games, we define notions of quantum non-local game homomorphisms and quantum non-local game isomorphisms, and show that games, isomorphic with respect to a given correlation type, have equal values and asymptotic values relative to this type. We examine a new class of no-signalling correlations, which witness the existence of non-local game homomorphisms, and characterise them in terms of states on tensor products of canonical operator systems. We define jointly synchronous correlations and show that they correspond to traces on the tensor product of the canonical C*-algebras associated with the game parties.
