Entropy of Quantum Markov states on Cayley trees

Abstract

In this paper, we continue the investigation of quantum Markov states (QMS) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The present work takes a huge leap forward at tackling one of the most important open problems in quantum probability which concerns the calculations of mean entropies of quantum Markov fields. Moreover, it opens new perspective for the generalization of many interesting results related to the one dimensional quantum Markov states and chains to multi-dimensional cases.

14 pages, JSTAT accepted

References in corpus (4)

• Diagonalizability of non homogeneous quantum Markov states and associated von Neumann algebras
• Quantum Markov States on Cayley trees
• Refinement of quantum Markov states on trees
• Quantum Markov Chains on the Comb graphs: Ising model