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.

arXiv:2609.08639 [quant-ph]

(or arXiv:2609.08639v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.08639 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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