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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Modulus of continuity of the quantum f-entropy with respect to the trace distance

arXiv
Authors: Iosif Pinelis

Year

2021

Paper ID

63031

Status

Preprint

Abstract Read

~2 min

Abstract Words

98

Citations

N/A

Abstract

A well-known result due to Fannes is a certain upper bound on the modulus of continuity of the von Neumann entropy with respect to the trace distance between density matrices; this distance is the maximum probability of distinguishing between the corresponding quantum states. Much more recently, Audenaert obtained an exact expression of this modulus of continuity. In the present note, Audenaert's result is extended to a broad class of entropy functions indexed by arbitrary continuous convex functions f in place of the Shannon--von Neumann function xmapsto xlog2x. The proof is based on the Schur majorization.

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  • A well-known result due to Fannes is a certain upper bound on the modulus of continuity of the von Neumann entropy with respect to the trace distance between density matrices...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2107.10112 [2] arXiv https://arxiv.org/abs/2107.10112 [3] Publisher https://arxiv.org/abs/2107.10112

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