General Continuity Bounds for Quantum Relative Entropies
Quantum Physics
2024-02-06 v3
Abstract
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we mostly recover known almost optimal bounds, whereas, for the Belavkin-Staszewski relative entropy, our bounds are new. Finally, we use these continuity bounds to derive a new entropic uncertainty relation.
Keywords
Cite
@article{arxiv.2305.10140,
title = {General Continuity Bounds for Quantum Relative Entropies},
author = {Andreas Bluhm and Ángela Capel and Paul Gondolf and Antonio Pérez-Hernández},
journal= {arXiv preprint arXiv:2305.10140},
year = {2024}
}
Comments
9 pages, 1 figure. This is a short version of the paper arXiv:2208.00922 with an additional new entropic uncertainty relation. v2,v3: We corrected a flaw in v1 of the paper