L 1 norm of coherence is not equal to its convex roof quantifier

Abstract

Since a rigorous framework for quantifying quantum coherence was established by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401), 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 , we call the corresponding convex roof quantifier of C. Whether 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 , it holds that .