开量子随机游动、量子马尔可夫链和常返性
Open Quantum Random Walks, Quantum Markov Chains and Recurrence
摘要：
本文构造了与开放量子随机游动相关的QMC，使得链的转移算子由OQRW定义，QMC对交换子代数的限制与OQRW的分布$P_ρ$一致.这为测度$P_ρ$的一些性质提供了新的线索。作为一个例子，我们简单地提到，该测度可以被认为是某些马尔可夫过程的某些函数的分布。此外，我们还研究了QMC和相关测度的一些性质。研究了QMC的一个新概念--$\f$ --常返性，并建立了所定义的常返性与已有常返性之间的关系。
英文摘要：
In the present paper, we construct QMCs associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution $P_ρ$ of OQRW. This sheds new light on some properties of the measure $P_ρ$. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov process. Furthermore, we study several properties of QMC and associated measure. A new notion of $\f$-recurrence of QMC is studied, and it is established relations between the defined recurrence and the existing ones.
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