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 |
|---|---|
| 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