Quantum Markov fields on graphs

Details Quantum Markov fields on graphs Quantum Markov fields on graphs

2009-11-09

arxiv.org/abs/0911.1667v2

Infinite Dimensional Analysis, Quantum Probability and Related Topics Vol. 13, No. 2 (2010) 165-189

Mathematics

Functional Analysis

23 pages, 1 figure. accepted to "Infinite Dimensional Anal. Quantum Probability & Related Topics"

Scientific paper

10.1142/S0219025710004000

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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