Optimal quantum channels

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.

Automated summary

A method for optimizing the cost of a quantum channel has been developed, with an emphasis on the role of entanglement in cost optimization. The approach can be applied to theoretically search for channels performing prescribed tasks while minimizing disturbance to the system's state.