The modified trace distance of coherence is constant on most pure states
Quantum Physics
2019-05-30 v1
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.
Keywords
Cite
@article{arxiv.1708.06967,
title = {The modified trace distance of coherence is constant on most pure states},
author = {Nathaniel Johnston and Chi-Kwong Li and Sarah Plosker},
journal= {arXiv preprint arXiv:1708.06967},
year = {2019}
}
Comments
5 pages, 3 figures