The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of being connected or not, and be allowed to merge, split and reconnect coherently in a superposition. Second, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates in a robust manner. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the neighbourhood and partitioning between systems become both quantum, dynamical, and logical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.

中文翻译：

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 量子网络理论


量子理论对离散系统的形式主义以两种重要方式进行了扩展。首先，量子进化被推广为作用于整个网络配置，因此节点可能会发现自己处于连接或未连接的量子叠加中，并被允许在叠加中连贯地合并、拆分和重新连接。其次，张量和追踪是通用的，因此可以根据几乎任意的逻辑谓词以稳健的方式对系统进行分区。特此提出的数学框架通过众多引理建立在坚实的基础之上。事实上，人们可能担心，随着系统之间的邻域和分区变得量子、动力学和逻辑，量子理论中标准的幺正性、完全正性、痕迹保留、非信号因果关系、局部性和局部性等概念之间熟悉的相互关系会受到威胁。这种相互关系实际上贯穿始终，尽管有两个新概念变得有用：一致性和理解。