Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical divergence for flat $\alpha$-connections: Classical and
  Quantum   A recent canonical divergence, which is introduced on a smooth manifold
$\mathrm{M}$ endowed with a general dualistic structure
$(\mathrm{g},\nabla,\nabla^*)$, is considered for flat $\alpha$-connections. In
the classical setting, we compute such a canonical divergence on the manifold
of positive measures and prove that it coincides with the classical
$\alpha$-divergence. In the quantum framework, the recent canonical divergence
is evaluated for the quantum $\alpha$-connections on the manifold of all
positive definite Hermitian operators. Also in this case we obtain that the
recent canonical divergence is the quantum $\alpha$-divergence.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom