Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparing coherence measures for X states: Can quantum states be ordered
  based on quantum coherence?   Quantum coherence is an essential resource for quantum information processing
and various quantitative measures of it have been introduced. However, the
interconnections between these measures are not yet understood properly. Here,
using a large set of randomly prepared $X$ states and analytically obtained
expressions of various measures of coherence (e.g., relative entropy of
coherence, $l1$ norm of coherence, coherence via skew information, and
first-order coherence), it is established that these measures of quantum
coherence cannot be used to perform ordering of a set of quantum states based
on the amount of coherence present in a state. Further, it is shown that for a
given value of quantum coherence measured by the relative entropy of coherence,
maximally nonlocal mixed states of $X$ type (which are characterized by maximal
violation of the CHSH inequality) have maximum quantum coherence as measured by
$l1$ norm of coherence. In addition, the amount of coherence measured by $l1$
norm of coherence for a Werner state is found to be always less than that for a
maximally nonlocal mixed state even when they possess an equal amount of
coherence measured by the relative entropy of coherence. These resource theory
based measures of coherence are not observed to show any relation with the
first-order coherence, while its maximum (hidden coherence) is found to be more
connected to concurrence both being basis independent quantities. These
observations could be of use in obtaining a deeper understanding of the
interconnections between various measures of quantum coherence.

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The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat