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Quantum Entropy Information Measures Entanglement Theory Quantum Correlations

Tight uniform continuity bound for a family of entropies

arXiv
Authors: Eric P. Hanson, Nilanjana Datta

Year

2017

Paper ID

44633

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, S_α, for αin (0,1). We establish necessary and sufficient conditions for equality in the continuity bound and prove that these conditions are the same for every member of the family. Our result builds on recent work in which we constructed a state which was majorized by every state in a neighbourhood $varepsilon$-ball of a given state, and thus was the minimal state in majorization order in the varepsilon-ball. This minimal state satisfies a particular semigroup property, which we exploit to prove our bound.

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  • We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, S_α, for αin (0,1).

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1707.04249 [2] arXiv https://arxiv.org/abs/1707.04249 [3] Publisher https://arxiv.org/abs/1707.04249

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