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General Continuity Bounds for Quantum Relative Entropies

Published 17 May 2023 in quant-ph | (2305.10140v3)

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.

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