标题： 因果顺序的量子控制路由 显示英文标题

标题： Routing Quantum Control of Causal Order

摘要： 近年来，已经提出了各种框架来研究具有不确定因果顺序的量子过程。 特别是，具有因果顺序量子控制的量子电路（QC-QCs）形成了一类从下到上构建的物理超图，并被认为代表了在固定时空内物理可实现的所有量子过程。 作为补充，路由量子电路的形式引入了受“路由”约束的量子操作，以更精细的路由电路分解方式来表示过程。 这种分解通过所谓的路由图进行形式化，表示各自过程中的信息流。 然而，到目前为止，仅对于一小部分过程证明了路由电路分解的存在性，包括一些特定的QC-QCs和更奇特的过程作为例子。 在本工作中，我们通过连接这两个框架来弥补这一不足。 我们证明，对于任何给定的$N$，可以使用一个单一的路由图系统地获得任何具有$N$个参与者的QC-QC的路由电路分解。 我们详细说明了这个构造，并将其与其他从替代路由图获得的QC-QC的路由电路分解进行对比。 最后，我们指出这种联系如何有助于解决不确定因果顺序领域中的各种开放问题，特别是建立QC-QC子类的电路表示。 显示英文摘要

摘要： In recent years, various frameworks have been proposed for the study of quantum processes with indefinite causal order. In particular, quantum circuits with quantum control of causal order (QC-QCs) form a broad class of physical supermaps obtained from a bottom-up construction and are believed to represent all quantum processes physically realisable in a fixed spacetime. Complementarily, the formalism of routed quantum circuits introduces quantum operations constrained by "routes" to represent processes in terms of a more fine-grained routed circuit decomposition. This decomposition, formalised using a so-called routed graph, represents the information flow within the respective process. However, the existence of routed circuit decompositions has only been established for a small set of processes so far, including both certain specific QC-QCs and more exotic processes as examples. In this work, we remedy this fact by connecting these two frameworks. We prove that for any given $N$, one can use a single routed graph to systematically obtain a routed circuit decomposition for any QC-QC with $N$ parties. We detail this construction explicitly and contrast it with other routed circuit decompositions of QC-QCs, which we obtain from alternative routed graphs. We conclude by pointing out how this connection can be useful to tackle various open problems in the field of indefinite causal order, particularly establishing circuit representations of subclasses of QC-QCs.