paper

Universal proofs of entropic continuity bounds via majorization flow

arXiv:1909.06981 · doi:10.4171/90-1/20

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-Rényi 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.

29 pages; v2: added Cor. 3.2, Section 7, shortened some proofs, minor fixes; v3: added Section 6.2, minor fixes

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