Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wigner function and the probability representation of quantum states   The relation of the Wigner function with the fair probability distribution
called tomographic distribution or quantum tomogram associated with the quantum
state is reviewed. The connection of the tomographic picture of quantum
mechanics with the integral Radon transform of the Wigner quasidistribution is
discussed. The Wigner--Moyal equation for the Wigner function is presented in
the form of kinetic equation for the tomographic probability distribution both
in quantum mechanics and in the classical limit of the Liouville equation. The
calculation of moments of physical observables in terms of integrals with the
state tomographic probability distributions is constructed having a standard
form of averaging in the probability theory. New uncertainty relations for the
position and momentum are written in terms of optical tomograms suitable for
direct experimental check. Some recent experiments on checking the uncertainty
relations including the entropic uncertainty relations are discussed.

26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
18
The categories of this paper are: econ
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph