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

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.04320
 Bibcode:
 2022arXiv220804320M
 Keywords:

 Mathematical Physics;
 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras;
 Quantum Physics;
 46L53;
 46L60;
 82B10;
 81Q10
 EPrint:
 17 pages