Quantum control of noisy channels

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.