  The traditional perspective in quantum resource theories concerns how to use
free operations to convert one resourceful quantum state to another one. For
example, a fundamental and well known question in entanglement theory is to
determine the distillable entanglement of a bipartite state, which is equal to
the maximum rate at which fresh Bell states can be distilled from many copies
of a given bipartite state by employing local operations and classical
communication for free. It is the aim of this paper to take this kind of
question to the next level, with the main question being: What is the best way
of using free channels to convert one resourceful quantum channel to another?
Here we focus on the the resource theory of entanglement for bipartite channels
and establish several fundamental tasks and results regarding it. In
particular, we establish bounds on several pertinent information processing
tasks in channel entanglement theory, and we define several entanglement
measures for bipartite channels, including the logarithmic negativity and the
$\kappa$-entanglement. We also show that the max-Rains information of [B\"auml
et al., Physical Review Letters, 121, 250504 (2018)] has a divergence
interpretation, which is helpful for simplifying the results of this earlier
work.
