Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the philosophy of Cram\'er-Rao-Bhattacharya Inequalities in Quantum
  Statistics   To any parametric family of states of a finite level quantum system we
associate a space of Fisher maps and introduce the natural notions of
Cram\'er-Rao-Bhattacharya tensor and Fisher information form. This leads us to
an abstract Cram\'er-Rao-Bhattacharya lower bound for the covariance matrix of
any finite number of unbiased estimators of parameteric functions. A number of
illustrative examples is included. Modulo technical assumptions of various
kinds our methods can be applied to infinite level quantum systems as well as
parametric families of classical probability distributions on Borel spaces.

3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg