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Tree-Homogeneous Quantum Markov Chains

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Abstract

We clarify the structure of tree-homogeneous quantum Markov chains (THQMC) as a multi-dimensional quantum extension of homogeneous Markov chains. We provide a construction of a class of quantum Markov chains on the Cayley tree based on open quantum random walks. Moreover, we prove the uniqueness of THQMC for the construction under consideration, which means the absence of phase transitions.

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Acknowledgements

The authors extend their appreciation to the Deputyship for Research& Innovation, Ministry of Education, Saudi Arabia for funding this researc h work through the project number (QU-IF-2-4-1-25343). The authors also thank to Qassim University for technical support.

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Authors and Affiliations

  1. Department of Management Information Systems, College of Business Management, Qassim University, 58611, ArRass, Saudi Arabia

    Abdessatar Souissi

  2. Department of Mathematics and Statistics, College of Science, King Faisal University, PO.Box: 400, Al-Ahsa, 31982, Saudi Arabia

    Abdessatar Souissi & Abdessatar Barhoumi

  3. Department of Mathematical Sciences, College of Science, United Arab Emirates University, 15551, Al-Ain, United Arab Emirates

    Farrukh Mukhamedov

  4. Institute of Mathematics named after V.I.Romanovski, 4, University, str., 100125, str., 100125, Tashkent, Uzbekistan

    Farrukh Mukhamedov

  5. LR18ES45, Mathematical Physics, Quantum Modeling and Mechanical Design, University of Carthage, Sidi Bou Said, Av. of the Republic, Carthage, 1054, Tunisia

    Abdessatar Barhoumi

Authors
  1. Abdessatar Souissi
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  2. Farrukh Mukhamedov
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  3. Abdessatar Barhoumi
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Contributions

A.S.: investigation; prepare the manuscript; F.M.: methodology, investigation; conceptualization, editing; A.B.: investigation; editing.

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Correspondence to Abdessatar Souissi.

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Souissi, A., Mukhamedov, F. & Barhoumi, A. Tree-Homogeneous Quantum Markov Chains. Int J Theor Phys 62, 19 (2023). https://doi.org/10.1007/s10773-023-05276-1

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