Optimal quantum channels
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.
Cite
@article{arxiv.2010.09519,
title = {Optimal quantum channels},
author = {Rocco Duvenhage},
journal= {arXiv preprint arXiv:2010.09519},
year = {2021}
}
Comments
v1: 5 pages. v2: More complete discussion of the role of entanglement. Faulty example extended to a separate section. Other minor additions and corrections. References added. 8 pages. v3: Some references and clarifying remarks added. Minor corrections made. 9 pages. v4: Minor typos (missing transposition signs) fixed at end of Sec. VI