Quantum Markov chains associated with open quantum random walks

Abstract

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.

30 pages

References in corpus (6)

• Open Quantum Random Walks
• Open Quantum Walks on Graphs
• On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two
• On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
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• Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory

Cited by in corpus (5)

• Review on Quantum Walk Computing: Theory, Implementation, and Application
• A Comparison of Quantum Walk Implementations on NISQ Computers
• Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
• Refinement of quantum Markov states on trees
• Quantum Markov Chains on the Comb graphs: Ising model