Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strengthened monotonicity inequality of quantum relative entropy: A
  unifying approach via R\'{e}nyi relative entropy   We derive a strengthened monotonicity inequality for quantum relative entropy
by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a
unifying treatment towards the improvement of some quantum entropy
inequalities. In particular, an emphasis is put on a lower bound of quantum
conditional mutual information (QCMI) as it gives a Pinsker-like lower bound
for the QCMI. We also give some improved entropy inequalities based on
R\'{e}nyi relative entropy. The inequalities obtained, thus, extends some
well-known ones. We also obtain a condition under which a tripartite operator
becomes a Markov state. As a by-product we provide some trace inequalities of
operators, which are of independent interest.

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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org