In the present paper we study a unified approach for Quantum Markov Chains. 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, including both Boson and Fermi algebras. The main result is a reconstruction theorem for quantum Markov chains in the mentioned kind of local algebras. Namely, this reconstruction allows the reproduction of all existing examples of quantum Markov chains and states.
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