Certifying optimality for convex quantum channel optimization problems
Abstract
We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for convex optimization problems over the set of all quantum measurements of a given system having a fixed number of measurement outcomes are obtained as a special case. In the case of linear objective functions for measurement optimization problems, our conditions reduce to the well-known Holevo-Yuen-Kennedy-Lax measurement optimality conditions. We illustrate how our conditions can be applied to various state transformation problems having non-linear objective functions based on the fidelity, trace distance, and quantum relative entropy.
Cite
@article{arxiv.1810.13295,
title = {Certifying optimality for convex quantum channel optimization problems},
author = {Bryan Coutts and Mark Girard and John Watrous},
journal= {arXiv preprint arXiv:1810.13295},
year = {2021}
}
Comments
29 pages