We review recent developments in the theory of quantum Markov states on the standard $\bz^{d}$--spin lattice. A Dobrushin theory for quantum Markov fields is proposed. In the one--di\-men\-sional case where the order plays a crucial role, the structure arising from a quantum Markov state is fully understood. In this situation we obtain a splitting of a Markov state into a classical part, and a purely quantum part. This result allows us to provide a reconstruction theorem for quantum Markov states on chains
Accardi, L., Fidaleo, F. (2002). Markov property: recent developments on the Quantum Markov property. In W. Freudenberg (a cura di), Quantum probability and infinite-dimensional analysis (pp. 1-19). World Scientific.
Markov property: recent developments on the Quantum Markov property
ACCARDI, LUIGI;FIDALEO, FRANCESCO
2002-01-01
Abstract
We review recent developments in the theory of quantum Markov states on the standard $\bz^{d}$--spin lattice. A Dobrushin theory for quantum Markov fields is proposed. In the one--di\-men\-sional case where the order plays a crucial role, the structure arising from a quantum Markov state is fully understood. In this situation we obtain a splitting of a Markov state into a classical part, and a purely quantum part. This result allows us to provide a reconstruction theorem for quantum Markov states on chainsFile | Dimensione | Formato | |
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