Quantum Markov fields on graphs
Functional Analysis
2012-04-10 v2 Mathematical Physics
math.MP
Operator Algebras
Probability
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 -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.
Keywords
Cite
@article{arxiv.0911.1667,
title = {Quantum Markov fields on graphs},
author = {Luigi Accardi and Hiromichi Ohno and Farrukh Mukhamedov},
journal= {arXiv preprint arXiv:0911.1667},
year = {2012}
}
Comments
23 pages, 1 figure. accepted to "Infinite Dimensional Anal. Quantum Probability & Related Topics"