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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
68/2018

Quantifying quantum coherence and non-classical correlation based on Hellinger distance

Zhi-Xiang Jin and Shao-Ming Fei

Abstract

Quantum coherence and non-classical correlation are key features of quantum world. Quantifying coherence and non-classical correlation are two key tasks in quantum information theory.

First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated.

Moreover, we present Hellinger distance-based measure of non-classical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, and but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit trade-off relation satisfied by the quantum coherence and this non-classical correlation.

Received:
Aug 20, 2018
Published:
Aug 28, 2018

Related publications

inJournal
2018 Repository Open Access
Zhi-Xiang Jin and Shao-Ming Fei

Quantifying quantum coherence and non-classical correlation based on Hellinger distance

In: Physical review / A, 97 (2018) 6, p. 062342