Abstract:
A method to optimize the cost of a quantum channel is developed. The goal is to determine the cheapest
channel that produces prescribed output states for a given set of input states. This is essentially a quantum
version of optimal transport. To attach a clear conceptual meaning to the cost, channels are viewed in terms of
what we call elementary transitions, which are analogous to point-to-point transitions between classical systems.
The role of entanglement in optimization of cost is emphasized. We also show how our approach can be applied
to theoretically search for channels performing a prescribed set of tasks on the states of a system, while otherwise
disturbing the state as little as possible.
