arXiv:0911.1667 · Infinite Dimensional Analysis Quantum Probability and Related Topics

QUANTUM MARKOV FIELDS ON GRAPHS

Luigi Accardi, Hiromichi Ohno, Farrukh Maksutovich Mukhamedov

Published Jun 1, 2010• 35 citations

Abstract

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

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