Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace-distance measure of coherence   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 $p\in(1,\infty)$.

14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an