Diagonalizability of Quantum Markov States on Trees

Farrukh Mukhamedov, Abdessatar Souissi

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We introduce quantum Markov states (QMS) in a general tree graph G= (V, E) , extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS φ on a UHF-algebra AV over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation E: AV→ DV such that φ=φ⌈DV∘E. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra DV.

Original languageEnglish
Article number9
JournalJournal of Statistical Physics
Issue number1
Publication statusPublished - Jan 2021


  • C-algebras
  • Conditional expectations
  • Localized
  • Maximal abelian subalgebra
  • Quantum Markov state
  • Tree
  • diagonalizability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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