Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Robertson-type Uncertainty Principle and Quantum Fisher Information   Let $A_1,...,A_N$ be complex selfadjoint matrices and let $\rho$ be a density
matrix. The Robertson uncertainty principle $$ det (Cov_\rho(A_h,A_j)) \geq det
(- \frac{i}{2} Tr (\rho [A_h,A_j])) $$ gives a bound for the quantum
generalized covariance in terms of the commutators $ [A_h,A_j]$. The right side
matrix is antisymmetric and therefore the bound is trivial (equal to zero) in
the odd case $N=2m+1$.
  Let $f$ be an arbitrary normalized symmetric operator monotone function and
let $<\cdot, \cdot >_{\rho,f}$ be the associated quantum Fisher information. In
this paper we prove the inequality $$ det (Cov_\rho (A_h,A_j)) \geq det
(\frac{f(0)}{2} < i[\rho, A_h],i[\rho,A_j] >_{\rho,f}) $$ that gives a
non-trivial bound for any $N \in {\mathbb N}$ using the commutators
$[\rho,A_h]$.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph