Abstract
We clarify the structure of tree-homogeneous quantum Markov chains (THQMC) as a multi-dimensional quantum extension of homogeneous Markov chains. We provide a construction of a class of quantum Markov chains on the Cayley tree based on open quantum random walks. Moreover, we prove the uniqueness of THQMC for the construction under consideration, which means the absence of phase transitions.
Original language | English |
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Article number | 19 |
Journal | International Journal of Theoretical Physics |
Volume | 62 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2023 |
Keywords
- Cayley tree
- Disordered phase
- Markov chains
- Random walks
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy (miscellaneous)