TY - JOUR
T1 - Open Quantum Random Walks and Quantum Markov chains on Trees I
T2 - Phase transitions
AU - Mukhamedov, Farrukh
AU - Souissi, Abdessatar
AU - Hamdi, Tarek
N1 - Funding Information:
The authors gratefully acknowledge Qassim University, represented by the Deanship of Scientific Research, on the financial support for this research under the number (10173-cba-2020-1-3-I) during the academic year 1442 AH/ 2020 AD.
Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/3/1
Y1 - 2022/3/1
N2 - 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.
AB - 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.
KW - Cayley tree
KW - Open quantum random walks
KW - disordered phase
KW - phase transition
KW - quantum Markov chain
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U2 - 10.1142/S1230161222500032
DO - 10.1142/S1230161222500032
M3 - Article
AN - SCOPUS:85137749157
SN - 1230-1612
VL - 29
JO - Open Systems and Information Dynamics
JF - Open Systems and Information Dynamics
IS - 1
M1 - 2250003
ER -