Open Quantum Random Walks and Quantum Markov Chains

Abstract

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 ℙ_ρ of the walk. This sheds new light on some properties of the measure ℙ_ρ. For example, this measure can be considered as the distribution of some functions of a certain Markov process.