  In this paper we construct (nonhomogeneous) quantum Markov chains associated
with open quantum random walks. The quantum Markov chain, like the classical
Markov chain, is a fundamental tool for the investigation of the basic
properties such as reducibility/irreducibility, recurrence/transience,
accessibility, ergodicity, etc, of the underlying dynamics. Here we focus on
the discussion of the reducibility and irreducibility of open quantum random
walks via the corresponding quantum Markov chains. Particularly we show that
the concept of reducibility/irreducibility of open quantum random walks in this
approach is equivalent to the one previously done by Carbone and Pautrat. We
provide with some examples. We will see also that the classical Markov chains
can be reconstructed as quantum Markov chains.
