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General Continuity Bounds for Quantum Relative Entropies
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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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The Alicki-Fannes-Winter technique in the quasi-classical settings: advanced version and its applications
An optimized version of the Alicki-Fannes-Winter technique yields strictly tighter semicontinuity and continuity bounds for several quantum and classical information characteristics.
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