Causal-Class Hierarchies in Coherence-Constrained Channel Transformation
Published in arXiv preprint, 2026
This work studies whether causal freedom improves channel transformation when the higher-order process is constrained by the resource theory of coherence. A unified semidefinite-programming framework reveals a strict hierarchy among parallel, fixed-order sequential, and general higher-order strategies for two qubit amplitude-damping channels. By contrast, mixed-Pauli channels admit a free program-state parallelization that makes all three causal classes equally effective for any target channel.