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Swapan Rana , Preeti Parashar , Maciej Lewenstein ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1103/physreva.93.012110 · OA: W2114659717

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 semi definite 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 $p\in(1,\infty)$.