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.

中文翻译：

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量子马尔可夫链：一种统一方法

在本文中，我们研究了量子马尔可夫链 (QMC) 的统一方法。讨论了一种新的量子马尔可夫性质，它概括了旧的性质。我们在一般局部代数上引入马尔可夫状态和链，具有一般代数性质。我们强调这种代数既包括玻色子代数也包括费米代数。我们的主要结果涉及量子马尔可夫链和量子马尔可夫状态的两个重建定理。即，我们通过例子来说明结果。