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arXiv:1808.03479 · Journal of Statistical Physics

Quantum Markov Chains Associated with Open Quantum Random Walks

Ameur Dhahri, Chul Ki Ko, Hyun Jae Yoo

Published Jun 21, 2019• 23 citations
arXivHTMLPDF
DOI
10.1007/s10955-019-02342-z

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In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. We then discuss the reducibility and irreducibility of open quantum random walks via the corresponding quantum Markov chains. The quantum Markov chain was introduced by Accardi by using transition expectation, and the construction of the quantum Markov chains for the open quantum random walks was introduced by Dhahri and Mukhamedov. Here we construct nonhomogeneous quantum Markov chains for the open quantum random walks so that we can naturally express the evolution of any open quantum random walk by the corresponding quantum Markov chain. We provide with some examples. In particular, we show that the classical Markov chains are reconstructed as quantum Markov chains as well and the reducibility and irreducibility properties of classical Markov chains can be investigated in the language of quantum Markov chains.