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.Comment: 23 pages, 1 figure. accepted to "Infinite Dimensional Anal. Quantum
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