Open Quantum Random Walks and Quantum Markov chains on Trees II: The recurrence

TL;DR

This paper constructs Quantum Markov Chains linked to Open Quantum Random Walks on trees, revealing phase transition phenomena and calculating mean entropies, advancing understanding of quantum stochastic processes.

Contribution

It introduces a new construction of Quantum Markov Chains on trees associated with OQRW, demonstrating phase transitions and computing mean entropies.

Findings

Detection of phase transition phenomena in QMCs on trees

Construction of QMCs associated with OQRW

Calculation of mean entropies of QMCs

Abstract

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 of OQRW. Furthermore, we first propose a new construction of QMC on trees, which is an extension of QMC considered in Ref. [9]. 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 first time in this direction. Moreover, mean entropies of QMCs are calculated.