TY - JOUR

T1 - Open quantum random walks, quantum Markov chains and recurrence

AU - Dhahri, Ameur

AU - Mukhamedov, Farrukh

N1 - Funding Information:
A. Dhahri acknowledges support by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (grant 2016R1C1B1010008).
Publisher Copyright:
© 2019 World Scientific Publishing Company.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - In the present paper, we construct QMCs (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 ρ of OQRW. This sheds new light on some properties of the measure ρ. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of φ-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

AB - In the present paper, we construct QMCs (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 ρ of OQRW. This sheds new light on some properties of the measure ρ. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of φ-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

KW - Open quantum random walk

KW - finitely correlated state

KW - quantum Markov chain

KW - recurrence

UR - http://www.scopus.com/inward/record.url?scp=85061234032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061234032&partnerID=8YFLogxK

U2 - 10.1142/S0129055X1950020X

DO - 10.1142/S0129055X1950020X

M3 - Article

AN - SCOPUS:85061234032

VL - 31

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 7

M1 - 1950020

ER -