Operational resource theory of quantum channels
This Letter proposes a general resource framework for quantum channels and introduces resource monotones based on general distance quantifiers of channels, and studies the interplay between channel and state resource theories by relating resourceMonotones of a quantum channel to its manipulation power of the state resource.
Abstract
Quantum resource theories have been widely studied to systematically\ncharacterize the non-classicality of quantum systems. Most resource theories\nfocus on quantum states and study their interconversions. Although quantum\nchannels are generally used as the tool for state manipulation, such a\nmanipulation capability can be naturally regarded as a generalized quantum\nresource, leading to an open research direction in the resource theories of\nquantum channels. Various resource-theoretic properties of channels have been\ninvestigated, however, without treating channels themselves as operational\nresources that can also be manipulated and converted. In this Letter, we\naddress this problem by first proposing a general resource framework for\nquantum channels and introducing resource monotones based on general distance\nquantifiers of channels. We study the interplay between channel and state\nresource theories by relating resource monotones of a quantum channel to its\nmanipulation power of the state resource. Regarding channels as operational\nresources, we introduce asymptotic channel distillation and dilution, the most\nimportant tasks in an operational resource theory, and show how to bound the\nconversion rates with channel resource monotones. Finally, we apply our results\nto quantum coherence as an example and introduce the coherence of channels,\nwhich characterizes the coherence generation ability of channels. We consider\nasymptotic channel distillation and dilution with maximally incoherent\noperations and find the theory asymptotically irreversible, in contrast to the\nasymptotic reversibility of the coherence of states.\n