arXiv:1811.00500 · Infinite Dimensional Analysis Quantum Probability and Related Topics

Quantum Markov chains: A unification approach

Luigi Accardi, Abdessatar Souissi, El Gheteb Soueidi

Published Jun 1, 2020• 38 citations

Abstract

In this paper, we study a unified approach for quantum Markov chains (QMCs). A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic algebraic property. We stress that this kind of algebras includes both Boson and Fermi algebras. Our main results concern two reconstruction theorems for quantum Markov chains and for quantum Markov states. Namely, we illustrate the results through examples.

DOI: 10.1142/s0219025720500162

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