Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1703.03265 · Quantum Information Processing

Notes on modified trace distance measure of coherence

Bin Chen, Shao-Ming Fei

Published Mar 22, 2018• 31 citations
arXivHTMLPDF
DOI
10.1007/s11128-018-1879-9

Related papers

Trace distance measure of coherence for a class of qudit states

Zhen Wang, Yan-Ling Wang, Zhi‐Xi Wang

arXiv:1610.07330•Quantum Information Processing•Sep 1, 2016•11 citations

Quantifying coherence of quantum channels via trace distance

Yajing Fan, Xia Guo, Xiaoyue Yang

Quantum Information Processing•Sep 29, 2022•6 citations

Coherence measures based on coherence eigenvalue and their applications

Lei Li, Qing‐Wen Wang, Shu‐Qian Shen +1 more

Quantum Information Processing•Oct 3, 2019•1 citation

The modified trace distance of coherence is constant on most pure states

Nathaniel Johnston, Chi-Kwong Li, Sarah Plosker

Abstract Recently, the much-used trace distance of coherence was shown to not be a proper measure of coherence, so a modification of it was proposed. We derive an explicit formula for this modified trace distance of coherence on pure states. Our formula shows that, despite satisfying the axioms of proper coherence measures, it is likely not a good measure to use, since it is maximal (equal to 1) on all except for an exponentially-small (in the dimension of the space) fraction of pure states.

arXiv:1708.06967•Journal of Physics A Mathematical and Theoretical•Dec 18, 2017•7 citations

Quantifying the coherence of pure quantum states

Jianxin Chen, Shane Grogan, Nathaniel Johnston +2 more

In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence. We then use this result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states. We define the trace distance of entanglement and show that it coincides with the trace distance of coherence for pure states. Finally, we give an alternate proof to a recent result that the ${\ensuremath{\ell}}_{1}$ measure of coherence of a pure state is never smaller than its relative entropy of coherence.

arXiv:1601.06269•Physical Review A•Oct 7, 2016•34 citations

Coherence by measurement

Gregor Weihs

Nature Physics•Oct 1, 2007•1 citation
In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence. We then use this result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states. We define the trace distance of entanglement and show that it coincides with the trace distance of coherence for pure states. Finally, we give an alternate proof to a recent result that the ${\ensuremath{\ell}}_{1}$ measure of coherence of a pure state is never smaller than its relative entropy of coherence.