Continuity of the relative entropy of resource-Reference-Cited by-同舟云学术

Continuity of the relative entropy of resource

Published:2024-05-29 Issue:05 Volume:22 Page:
ISSN:0219-7499
Container-title:International Journal of Quantum Information
language:en
Short-container-title:Int. J. Quantum Inform.

Author:

Lami Ludovico¹^ORCID,Shirokov Maksim²^ORCID

Affiliation:

1. Korteweg–de Vries Institute for Mathematics, Institute for Theoretical Physics, and QuSoft, University of Amsterdam, the Netherlands

2. Steklov Mathematical Institute and Moscow Institute of Physics and Technology, Moscow, Russia

Abstract

We present a criterion to establish the local continuity of the relative entropy of resource, i.e. the relative entropy distance to the set of free states, in any quantum resource theory. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.

Funder

Freie Universität Berlin for hospitality during

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219749924400094

Reference24 articles.

1. Quantum resource theories

2. Quantifying Entanglement

3. Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints

4. Conditional expectation in an operator algebra. IV. Entropy and information

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