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.
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BibTeX
@misc{wei2026extensibly,
title = {{Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order}},
author = {Wenjie Wei and Shengshi Pang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18559},
eprint = {2609.18559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18559},
}
RIS
TY - UNPB
TI - Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order
AU - Wenjie Wei
AU - Shengshi Pang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18559
UR - https://arxiv.org/abs/2609.18559
AB - 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.
ER -