Open Quantum Random Walks, Quantum Markov Chains and Recurrence

2016/08/03 by Dhahri, Ameur, Mukhamedov, Farrukh
#46A37 #46L35 #46L55 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1608.01065

Abstract

In the present paper, we construct QMCs 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 P_ρ of OQRW. This sheds new light on some properties of the measure P_ρ. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov process. Furthermore, we study several properties of QMC and associated measure. A new notion of \f-recurrence of QMC is studied, and it is established relations between the defined recurrence and the existing ones.

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