Search

MiS Preprint Repository

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
7/2018

Max-relative Entropy of Coherence: An Operational Coherence Measure

Kaifeng Bu, Uttam Singh, Shao-Ming Fei, Arun Kumar Pati and Junde Wu

Abstract

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence.

We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of max-relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states.

This advantage of coherent states in subchannel discrimination can be exactly characterized by the max-relative entropy of coherence.

By introducing suitable smooth max-relative entropy of coherence, we prove that the smooth max-relative entropy of coherence provides a lower bound of one-shot coherence cost, and the max-relative entropy of coherence is equivalent to the relative entropy of coherence in asymptotic limit.

Similar to max-relative entropy of coherence, min-relative entropy of coherence has also been investigated. We show that the min-relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in asymptotic limit the min-relative entropy of coherence is equivalent to the relative entropy of coherence.

Received:
Jan 15, 2018
Published:
Jan 22, 2018

Related publications

inJournal
2017 Repository Open Access
Kaifeng Bu, Uttam Singh, Shao-Ming Fei, Arun Kumar Pati and Junde Wu

Maximum relative entropy of coherence : an operational coherence measure

In: Physical review letters, 119 (2017) 15, p. 150405