Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions

Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi

Research output: Contribution to journalArticlepeer-review

Abstract

In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution ℙp of OQRW. However, we are going to look at the probability distribution as a Markov field over the Cayley tree. Such kind of consideration allows us to investigate phase transition phenomena associated for OQRW within QMC scheme. Furthermore, we first propose a new construction of QMC on trees, which is an extension of QMC considered in [10]. Using such a construction, we are able to construct QMCs on tress associated with OQRW. Our investigation leads to the detection of the phase transition phenomena within the proposed scheme. This kind of phenomena appears for the first time in this direction. Moreover, mean entropies of QMCs are calculated.

Original languageEnglish
Article number2250003
JournalOpen Systems and Information Dynamics
Volume29
Issue number1
DOIs
Publication statusPublished - Mar 1 2022

Keywords

  • Cayley tree
  • disordered phase
  • Open quantum random walks
  • phase transition
  • quantum Markov chain

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics

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