Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reversibility of distance mesures of states with some focus on total
  variation distance   Consider a classical system, which is in the state described by probability
distribution $p$ or $q$, and embed these classical informations into quantum
system by a physical map $\Gamma$, $\rho=\Gamma(p)$ and $\sigma=\Gamma(q)$.
Intuitively, the pair $\{p_{\rho}^{M},p_{\sigma}^{M}\}$ of the distributions of
the data of the measurement $M$ on the pair $\{\rho,\sigma\}$ should contain
strictly less information than the pair $\{p,q\}$ provided the pair
$\{\rho,\sigma\}$ is non-commutative. Indeed, this statement had been shown if
the information is measured by $f$-divergence such that $f$ is operator convex.
In the paper, the statement is extended to the case where $f$ is strictly
convex. Also, we disprove the assertion for the total variation distance $\Vert
p-q\Vert_{1}$, the $f$-divergence with $f(r)=|1-r|$: if $\{\rho,\sigma\}$
satisfies some not very restrictive conditions, $\Vert
p_{\rho}^{M}-p_{\sigma}^{M}\Vert_{1}$ equals $\Vert p-q\Vert_{1}$. Here we
present sufficient condition for general case, and necessary and sufficient
condition for qubit states.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex