可扩展因果可分过程可实现为具有因果顺序经典控制的量子电路
Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order
- School of Physics, Sun Yat-sen University（中山大学物理学院）
- Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过广义隐形传态构造，证明每个多部分可扩展因果可分过程都能实现为具有因果顺序经典控制的量子电路，解决了长期开放问题，并给出了精确的操作性解释。
AI中文摘要：
不定因果顺序通过允许局部量子操作在没有预定全局顺序的情况下连接，扩展了传统电路范式。在过程矩阵框架中，它通过因果不可分性来表征，而可扩展因果可分性（ECS）要求，在任意输入辅助比特扩展下，一个过程允许递归分解为各个组件，每个组件与首先作用的特定操作兼容。具有因果顺序经典控制的量子电路（QC-CC），其中先前的结果动态决定下一步执行哪个操作，已知能生成ECS过程，但每个ECS过程是否都允许这样的实现一直是一个长期未解决的开放问题。我们通过一种广义隐形传态构造解决了这个问题，该构造将每个多部分ECS过程实现为QC-CC。我们进一步确立了平凡和非平凡全局过去与未来系统的ECS定义之间的一致性。这些结果为ECS提供了精确的操作性解释，并将QC-CC确定为这类过程背后的完整电路结构。
英文摘要：
Indefinite causal order extends the conventional circuit paradigm by allowing local quantum operations to be connected without a predetermined global order. Within the process-matrix framework, it is characterized by causal nonseparability, whereas extensible causal separability (ECS) requires that, under arbitrary input-ancilla extensions, a process admit a recursive decomposition into components, each compatible with a particular operation acting first. Quantum circuits with classical control of causal order (QC-CC), in which previous outcomes dynamically determine which operation acts next, are known to generate ECS processes, but whether every ECS process admits such a realization has remained a longstanding open problem. We settle it through a generalized teleportation construction that realizes every multipartite ECS process as a QC-CC. We further establish consistency between ECS definitions for trivial and nontrivial global past and future systems. These results provide ECS with an exact operational interpretation and identify QC-CC as the complete circuit structure underlying this class of processes.
