General Continuity Bounds for Quantum Relative Entropies
arXiv:2305.10140 · doi:10.1109/ISIT54713.2023.10206734
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.
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