Quantum resource theories have been widely studied to systematically characterize the nonclassicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are generally used as a tool for state manipulation, such a manipulation capability can be naturally regarded as a generalized quantum resource, leading to an open research direction in the resource theories of quantum channels. Various resource-theoretic properties of the channels have been investigated, however, without treating the channels themselves as operational resources that can also be manipulated and converted. In this Rapid Communication, we address this problem by first proposing a general resource framework for quantum channels and introducing resource monotones based on general distance quantifiers of the channels. We study the interplay between the channel and state resource theories by relating the resource monotones of a quantum channel to its manipulation power of the state resource. Regarding channels as operational resources, we introduce asymptotic channel distillation and dilution, the most important tasks in an operational resource theory, and show how to bound the conversion rates with the channel resource monotones. Finally, we apply our results to quantum coherence as an example and introduce the coherence of channels, which characterizes the coherence generation ability of channels. We consider asymptotic channel distillation and dilution with maximally incoherent operations and find the theory asymptotically irreversible, in contrast to the asymptotic reversibility of the coherence of states.

• Received 19 May 2019
• Accepted 7 January 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.012035

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society