Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification and characterization of quantum parametric models in
  quantum estimation theory   In this paper, we characterize quantum parametric models into different
classes based on the estimation error bound, known as the Holevo bound. These
classes are given by the classical, quasi-classical, D-invariant, and
asymptotically classical models. We first explore the relationships among these
four models and show that: i) The classical model having the diagonal elements
only is characterized by the intersection of the D-invariant and asymptotically
classical models. ii) There exists a gap between the classical model and the
quasi-classical model, where all logarithmic derivative operators commute with
each other. Further, we characterize each class with several equivalent
conditions. This result then reveals the geometrical understanding of quantum
statistical models.

0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn