Universal proofs of entropic continuity bounds via majorization flow

Eric P. Hanson; Nilanjana Datta

doi:10.4171/90-1/20

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arXiv · 1909.06981

Universal proofs of entropic continuity bounds via majorization flow

Eric P. Hanson·Nilanjana Datta

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Abstract

We introduce a notion of majorization flow, and demonstrate it to be a powerful tool for deriving simple and universal proofs of continuity bounds for entropic functions relevant in information theory. In particular, for the case of the alpha-R\'enyi entropy, whose connections to thermodynamics are discussed in this article, majorization flow yields a Lipschitz continuity bound for the case alpha > 1, thus resolving an open problem and providing a substantial improvement over previously known bounds.

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Eric P. Hanson, Nilanjana Datta. 2019-09-16. Universal proofs of entropic continuity bounds via majorization flow. https://doi.org/10.4171/90-1/20

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