Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Forward Quantum Markov Field on Graphs   In this paper, we propose a class of quantum Markov fields QMF on a graphs
$G= (V,E)$. The Markov structure of the considered QMF is investigated in the
finer structure of a quasi-local algebrav $\mathcal{A}_V$ of observables based
over a graphs $G$.
  Namely, the considered Markovian fields are infinite volume states defined
through a generating couple
  $(\varphi^{(0)}, (\mathcal{E}_{\{y\}\cup N_y}))$ of a product state
$\varphi^{(0)}$ on $\mathcal{A}_V$ and a family of local transition
expectations $\mathcal{E}_{\{y\}\cup N_y}$ based on a vertex $y$ and the set of
it nearest-neighbors.
  The main result of the paper concerns the existence and the uniqueness of QMF
associated with a couple $(\varphi^{(0)}, (\mathcal{E}_{\{y\}\cup N_y}))$ for
on an important class of graphs including trees strictly.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat