Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized uncertainty relations and efficient measurements in quantum
  systems   We consider two variants of a quantum-statistical generalization of the
Cramer-Rao inequality that establishes an invariant lower bound on the mean
square error of a generalized quantum measurement. The proposed complex variant
of this inequality leads to a precise formulation of a generalized uncertainty
principle for arbitrary states, in contrast to Helstrom's symmetric variant in
which these relations are obtained only for pure states. A notion of canonical
states is introduced and the lower mean square error bound is found for
estimating of the parameters of canonical states, in particular, the canonical
parameters of a Lie group. It is shown that these bounds are globally
attainable only for canonical states for which there exist efficient
measurements or quasimeasurements.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol