Quantum Markov Chains Associated with Open Quantum Random Walks

Ameur Dhahri, Chul Ki Ko, Hyun Jae Yoo

Research output: Contribution to journalArticle

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 of the underlying dynamics such as reducibility/irreducibility, recurrence/transience, accessibility, ergodicity, etc. So, the quantum Markov chain machinery opens many new features of the dynamics. On the other hand, as will be shown in this paper, the open quantum random walks serves as a very interesting nontrivial model for which one can construct the associated quantum Markov chains. Here, after constructing the quantum Markov chain associated with the open quantum random walks, 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 see also that the classical Markov chains can be reconstructed as quantum Markov chains.

Original languageEnglish
Pages (from-to)1272-1295
Number of pages24
JournalJournal of Statistical Physics
Volume176
Issue number5
DOIs
Publication statusPublished - 2019 Sep 1

Fingerprint

Markov chains
random walk
Random walk
Markov chain
Irreducibility
Reducibility
machinery
Transience
Ergodicity
Accessibility
Recurrence

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Dhahri, Ameur ; Ko, Chul Ki ; Yoo, Hyun Jae. / Quantum Markov Chains Associated with Open Quantum Random Walks. In: Journal of Statistical Physics. 2019 ; Vol. 176, No. 5. pp. 1272-1295.
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Quantum Markov Chains Associated with Open Quantum Random Walks. / Dhahri, Ameur; Ko, Chul Ki; Yoo, Hyun Jae.

In: Journal of Statistical Physics, Vol. 176, No. 5, 01.09.2019, p. 1272-1295.

Research output: Contribution to journalArticle

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