Related papers: $l_{1}$ norm of coherence is not equal to its convex roof quantifier

$l_{1}$ norm of coherence is not equal to its convex roof quantifier

URL: http://arxiv.org/abs/2110.10891v1
Date: Thu, 21 Oct 2021 04:34:25 GMT
Title: $l_{1}$ norm of coherence is not equal to its convex roof quantifier
Authors: Jianwei Xu
Abstract summary: We show that for the widely used coherence measure, $l_1$ norm of coherence $C_l_1$, it holds that $C_l_1neq overlineC_l_1$.
Score: 0.6091702876917281
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Since a rigorous framework for quantifying quantum coherence was established by Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)], many coherence measures have been found. For a given coherence measure $C$, extending the values of $C$ on pure states to mixed states by the convex roof construction, we will get a valid coherence measure $\overline{C}$, we call $\overline{C}$ the corresponding convex roof quantifier of $C$. Whether $C=\overline{C}$ for a given coherence measure is an important question. In this work, we show that for the widely used coherence measure, $l_{1}$ norm of coherence $C_{l_{1}}$, it holds that $C_{l_{1}}\neq \overline{C_{l_{1}}}$.

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