Trace-distance measure of coherence 论文

摘要

We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, $X$ states. An expression for the trace distance coherence for all pure states and a semidefinite program for arbitrary states is provided. We also explore the relation between ${l}_{1}$-norm and relative entropy based measures of coherence, and give a sharp inequality connecting the two. In addition, it is shown that both ${l}_{p}$-norm- and Schatten-$p$-norm--based measures violate the (strong) monotonicity for all $p\ensuremath{\in}(1,\ensuremath{\infty})$.