  Quantum resource theories have been widely studied to systematically
characterize the non-classicality of quantum systems. Most resource theories
focus on quantum states and study their interconversions. Although quantum
channels are generally used as the 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 channels have been
investigated, however, without treating channels themselves as operational
resources that can also be manipulated and converted. In this Letter, we
address this problem by first proposing a general resource framework for
quantum channels and introducing resource monotones based on general distance
quantifiers of channels. We study the interplay between channel and state
resource theories by relating 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 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.
