Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order

Abstract: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.

arXiv:2609.18559 [quant-ph]

(or arXiv:2609.18559v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.18559 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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