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 chains
2002
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Rilevanza internazionale
Capitolo o saggio
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.
Accardi, L; Fidaleo, F
Contributo in libro
File in questo prodotto:
File Dimensione Formato  
AcFid02_Markov property.pdf

accesso aperto

Dimensione 319.77 kB
Formato Adobe PDF
319.77 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/74527
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact