Refinement of quantum Markov states on trees

Abstract

In the present paper, we propose a refinement for the notion of quantum Markov states (QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any restriction of QMS in the sense of Ref. \cite{AccFid03} is not necessarily to be a QMS. It turns out that localized QMS has the mentioned property which is called \textit{sub-Markov states}, this allows us to characterize translation invariant QMS on regular trees.

17 pages

References in corpus (4)

• On the three state Potts model with competing interactions on the Bethe lattice
• Diagonalizability of non homogeneous quantum Markov states and associated von Neumann algebras
• Quantum Markov States on Cayley trees
• Block Markov Chains on Trees

Cited by in corpus (1)

• Entropy of Quantum Markov states on Cayley trees