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arXiv · 0911.1667

Quantum Markov fields on graphs

Luigi Accardi·Hiromichi Ohno·Farrukh Mukhamedov
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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.

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Luigi Accardi, Hiromichi Ohno, Farrukh Mukhamedov. 2010-01-18. Quantum Markov fields on graphs. https://doi.org/10.1142/s0219025710004000

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