Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric approach to quantum statistical inference   We study quantum statistical inference tasks of hypothesis testing and their
canonical variations, in order to review relations between their corresponding
figures of merit---measures of statistical distance---and demonstrate the
crucial differences which arise in the quantum regime in contrast to the
classical setting. In our analysis, we primarily focus on the geometric
approach to data inference problems, within which the aforementioned measures
can be neatly interpreted as particular forms of divergences that quantify
distances in the space of probability distributions or, when dealing with
quantum systems, of density matrices. Moreover, with help of the standard
language of Riemannian geometry we identify both the metrics such divergences
must induce and the relations such metrics must then naturally inherit.
Finally, we discuss exemplary applications of such a geometric approach to
problems of quantum parameter estimation, "speed limits" and thermodynamics.

36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th