Diagonalizability of Quantum Markov States on Trees

@article{Mukhamedov2019DiagonalizabilityOQ,
  title={Diagonalizability of Quantum Markov States on Trees},
  author={Farrukh Mukhamedov and Abdessatar Souissi},
  journal={Journal of Statistical Physics},
  year={2019},
  volume={182},
  pages={1-15}
}
We introduce quantum Markov states (QMS) in a general tree graph $$G= (V, E)$$ 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 $$\varphi $$ φ on a UHF-algebra $${\mathcal {A}}_V$$ A V over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the… 

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