Optimal quantum channels

TL;DR

This paper introduces a quantum optimal transport method to find the least costly quantum channels that transform specific input states into desired output states, emphasizing the role of entanglement and minimal disturbance.

Contribution

It develops a novel quantum optimal transport framework for channel cost optimization, incorporating elementary transitions and entanglement considerations.

Findings

Method effectively minimizes quantum channel costs for prescribed state transformations.

Entanglement plays a crucial role in optimizing quantum channel costs.

Applicable to designing channels for specific quantum tasks with minimal disturbance.

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.