QUANTUM MARKOV FIELDS ON GRAPHS

LUIGI ACCARDI, HIROMICHI OHNO, FARRUKH MUKHAMEDOV
2010 Infinite Dimensional Analysis Quantum Probability and Related Topics  
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on C^*-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
doi:10.1142/s0219025710004000 fatcat:cuytc7imvvbkzpzyxf3xfitvqq