Causal-Class Hierarchies in Coherence-Constrained Channel Transformation
Abstract
Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.
Related
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BibTeX
@misc{zhu2026causalclass,
title = {{Causal-Class Hierarchies in Coherence-Constrained Channel Transformation}},
author = {Lin Zhu and Benchi Zhao and Xuanqiang Zhao and Ranyiliu Chen and Xin Wang and Shenggen Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08639},
eprint = {2609.08639},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08639},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Causal-Class Hierarchies in Coherence-Constrained Channel Transformation
AU - Lin Zhu
AU - Benchi Zhao
AU - Xuanqiang Zhao
AU - Ranyiliu Chen
AU - Xin Wang
AU - Shenggen Zheng
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08639
UR - https://arxiv.org/abs/2609.08639
AB - Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.
ER -