  Sender and receiver can control noisy channels by means of the resources they
own, that is local operations, potentially correlated using classical
communication, and entangled pairs shared between them. Using the
Choi-Jamiolkowski isomorphism, we express the control of a noisy channel in
terms of control of (non-normalized) states, and show how the available
resources enter the analysis. Our formalism provides a general scheme for the
protection of quantum state transmission when a single use of the physical
channel is considered. Moreover, it paves the way to the application of control
theoretical tools to the study of noisy channels. We define the notion of
complexity of a noisy channel, as a measure of how demanding is to engineer
specific manipulations of a channel. We provide some examples of both
deterministic and probabilistic protocols leading to a decreased complexity.
