All causally separable quantum processes are quantum circuits with classical control of causal order
Abstract
The concept of causal (non)separability describes whether the causal order between parties that perform local quantum operations is well-defined or indefinite. Causal (non)separability in the general multipartite setting was introduced and studied in [Oreshkov and Giarmatzi, New J. Phys. 18, 093020 (2016); Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)]. We resolve an open problem from these earlier works by showing -- using a novel "coherent teleportation technique" -- that a sufficient condition for causal separability identified in [Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)] is also necessary, and thus provides a complete characterisation of multipartite causal separability. A consequence of this result is that all causally separable processes admit a realisation as generalised quantum circuits in which the order between the operations is classically controlled, known as "quantum circuits with classical control of causal order".
Related
- Extensibly Causally Separable Processes Admit Realizations as Quantum Circuits with Classical Control of Causal Order
- Quantum simulation of classical RCL circuits via complexification and Schrödingerization
- Complex Quantum Dynamics Versus Classical Simulability of Noisy Random Circuits
- A polynomial-time classical sampler for noisy quantum circuits from statistical mechanics
- Classical Pre-Training of Large Shallow Parametrized Quantum Circuits through Pauli Propagation and deployment on Quantum Hardware
BibTeX
@misc{wechs2026causally,
title = {{All causally separable quantum processes are quantum circuits with classical control of causal order}},
author = {Julian Wechs and Alastair A. Abbott and Cyril Branciard},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20774},
eprint = {2609.20774},
archivePrefix = {arXiv},
url = {https://inria.hal.science/hal-05759336v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - All causally separable quantum processes are quantum circuits with classical control of causal order
AU - Julian Wechs
AU - Alastair A. Abbott
AU - Cyril Branciard
PY - 2026
DA - 2026/09/17
PB - HAL
DO - 10.48550/arxiv.2609.20774
UR - https://inria.hal.science/hal-05759336v1
AB - The concept of causal (non)separability describes whether the causal order between parties that perform local quantum operations is well-defined or indefinite. Causal (non)separability in the general multipartite setting was introduced and studied in [Oreshkov and Giarmatzi, New J. Phys. 18, 093020 (2016); Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)]. We resolve an open problem from these earlier works by showing -- using a novel "coherent teleportation technique" -- that a sufficient condition for causal separability identified in [Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)] is also necessary, and thus provides a complete characterisation of multipartite causal separability. A consequence of this result is that all causally separable processes admit a realisation as generalised quantum circuits in which the order between the operations is classically controlled, known as "quantum circuits with classical control of causal order".
ER -