General Continuity Bounds for Quantum Relative Entropies

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.

arXiv comment9 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

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Cited by in corpus (6)

• Continuity of quantum entropic quantities via almost convexity
• Continuity bounds on observational entropy and measured relative entropies
• Continuity bounds for quantum entropies arising from a fundamental entropic inequality
• Unified framework for continuity of sandwiched Rényi divergences
• Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
• Belavkin-Staszewski Quantum Markov Chains