Extension to other dynamical resource theories

Determine how the comparison among parallel, fixed-order sequential, and general higher-order channel-transformation strategies changes when the coherence constraint is replaced by dynamical resource theories of entanglement, asymmetry, athermality, or magic.

Background

The paper studies causal hierarchies while imposing either maximally incoherent superchannels (MISC) or dephasing-covariant incoherent superchannels (DISC), both within the dynamical resource theory of coherence. It establishes that amplitude-damping channels retain a strict causal hierarchy under both free-operation classes, whereas mixed-Pauli channels exhibit collapse through free teleportation-based program-state simulation.

The authors explicitly leave unresolved whether analogous causal advantages, structural collapse conditions, and robustness under stricter free-operation constraints arise for other dynamical resources. The proposed extensions include entanglement, asymmetry, athermality, and magic, while preserving the paper’s separation between causal constraints and resource-theoretic constraints.