Relative entropies of quantum channels with applications in resource theory

TL;DR

This paper extends entropic measures from quantum states to channels, developing a framework for hypothesis testing, resource theories, and analyzing properties like entanglement and coherence of quantum channels.

Contribution

It introduces relative entropies for quantum channels, defines their entropy, and applies these concepts to resource theories and properties like entanglement and coherence.

Findings

Defined relative entropies of channels for hypothesis testing.

Established properties of these entropies and their relation to entanglement.

Proposed resource theories based on channel entropies.

Abstract

Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs. In this work, we extend the entropic quantifiers of states to the ones of channels. In the one-shot and asymptotic scenarios, we propose relative entropies of channels under the task of hypothesis testing. Then, we define the entropy of channels based on relative entropies from the target channel to the completely depolarising channel. We also study properties of relative entropies of channels and the interplay with entanglement. Finally, based on relative entropies of channels, we propose general resource theories of channels and discuss the coherence of general channels and measurements, and the entanglement of channels.