Quantum markov fields on graphs

Luigi Accardi, Hiromichi Ohno, Farrukh Mukhamedov

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)165-189
Number of pages25
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Issue number2
Publication statusPublished - Jun 2010
Externally publishedYes


  • Cayley tree
  • Generalized Markov state
  • d-Markov chains
  • entangled Markov fields
  • graph

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics


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