Quantum Markov fields on graphs - Accardi, Luigi; Ohno, Hiromichi; Mukhamedov, Farrukh (World Scientific Publishing, 2010)
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.