Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreducible decompositions and stationary states of quantum channels   For a quantum channel (completely positive, trace-preserving map), we prove a
generalization to the infinite dimensional case of a result by Baumgartner and
Narnhofer. This result is, in a probabilistic language, a decomposition of a
general quantum channel into its irreducible positive recurrent components.
This decomposition is related with a communication relation on the reference
Hilbert space. This allows us to describe the full structure of invariant
states of a quantum channel, and of their supports.

7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
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
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys