Open quantum random walks and quantum Markov chains. (English. Russian original) Zbl 1447.46050
Funct. Anal. Appl. 53, No. 2, 137-142 (2019); translation from Funkts. Anal. Prilozh. 53, No. 2, 72-78 (2019).
Summary: In the present paper we construct quantum Markov chains associated with open quantum random walks in the sense that the transition operator of a chain is determined by an open quantum random walk and the restriction of the chain to the commutative subalgebra coincides with the distribution \(\mathbb{P} _ \rho\) of the walk. This sheds new light on some properties of the measure \(\mathbb{P} _ \rho \). For example, this measure can be considered as the distribution of some functions of a certain Markov process.
MSC:
| 46L53 | Noncommutative probability and statistics |
References:
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