Tree-Homogeneous Quantum Markov Chains

Abdessatar Souissi; Farrukh Mukhamedov; Abdessatar Barhoumi

doi:10.1007/s10773-023-05276-1

Tree-Homogeneous Quantum Markov Chains

Abdessatar Souissi, Farrukh Mukhamedov, Abdessatar Barhoumi

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Article number	19
Journal	International Journal of Theoretical Physics
Volume	62
Issue number	2
DOIs	https://doi.org/10.1007/s10773-023-05276-1
Publication status	Published - Feb 2023

Keywords

Cayley tree
Disordered phase
Markov chains
Random walks

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy (miscellaneous)

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10.1007/s10773-023-05276-1

Cite this

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title = "Tree-Homogeneous Quantum Markov Chains",

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.",

keywords = "Cayley tree, Disordered phase, Markov chains, Random walks",

author = "Abdessatar Souissi and Farrukh Mukhamedov and Abdessatar Barhoumi",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Souissi, Abdessatar

AU - Mukhamedov, Farrukh

AU - Barhoumi, Abdessatar

N1 - Funding Information: 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. Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - Cayley tree

KW - Disordered phase

KW - Markov chains

KW - Random walks

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ER -

Tree-Homogeneous Quantum Markov Chains

Abstract

Keywords

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