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Quantum Skew Divergence

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arxiv 1304.5935 v2 pith:FYTAZXP7 submitted 2013-04-22 math-ph math.MP

Koenraad M.R. Audenaert This is my paper · ORCID
classification math-phmath.MP
keywords divergencequantumskewapplicationsbravyiconjecturecontextcontinuity
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In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum skew divergence, including its relation to other state distinguishability measures. Finally, we present a number of important applications: new continuity inequalities for the quantum Jensen-Shannon divergence and the Holevo information, and a new and short proof of Bravyi's Small Incremental Mixing conjecture.

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  1. Upper bounds on the Holevo quantity arising from the fundamental entropic inequality

    quant-ph 2025-06 conditional novelty 5.0 of 10

    A general inequality bounds the Holevo quantity of any quantum ensemble by a combination of the Holevo quantities of two auxiliary ensembles plus a mean binary entropy term, yielding simple distance-based upper bounds.

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