Application of the Resource Theory of Channels to Communication Scenarios

TL;DR

This paper develops a resource theory of quantum channels focusing on constant channels as free resources, providing new bounds and insights for quantum communication capacities and channel simulation with non-signalling assistance.

Contribution

It introduces a resource theory framework for channels, linking it to quantum Shannon theory, and offers new bounds and characterizations for communication and simulation tasks.

Findings

Converse bound for one-shot non-signalling assisted classical capacity

Strong converse property for the capacity

Characterization of channel simulation cost with non-signalling assistance

Abstract

We introduce a resource theory of channels relevant to communication via quantum channels, in which the set of constant channels --- useless channels for communication tasks --- is considered as the free resource. We find that our theory with such a simple structure is useful to address central problems in quantum Shannon theory --- in particular, we provide a converse bound for the one-shot non-signalling assisted classical capacity that naturally leads to its strong converse property, as well as obtain the one-shot channel simulation cost with non-signalling assistance. We clarify an intimate connection between the non-signalling assistance and our formalism by identifying the non-signalling assisted channel coding with the channel transformation under the maximal set of resource non-generating superchannels, providing a physical characterization of the latter. Our results provide new perspectives and concise arguments to those problems, connecting the recently developed fields of resource theories to `classic' settings in quantum information theory and shedding light on the validity of resource theories of channels as effective tools to address practical problems.