Abstract
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on C*-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
Original language | English |
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Pages (from-to) | 165-189 |
Number of pages | 25 |
Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |
Volume | 13 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 2010 |
Externally published | Yes |
Keywords
- Cayley tree
- Generalized Markov state
- d-Markov chains
- entangled Markov fields
- graph
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics