Trace-distance measure of coherence

Swapan Rana; Preeti Parashar; Maciej Lewenstein

doi:10.1103/physreva.93.012110

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arXiv · 1511.01854

Trace-distance measure of coherence

Swapan Rana·Preeti Parashar·Maciej Lewenstein

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Abstract

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

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Swapan Rana, Preeti Parashar, Maciej Lewenstein. 2016-01-21. Trace-distance measure of coherence. https://doi.org/10.1103/physreva.93.012110

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