caa a22 4500 378920758 CHVBK 20180305123604.0 cr unu---uuuuu 161128e20041201xx s 000 0 eng 10.1515/1569397042722328 doi (NATIONALLICENCE)gruyter-10.1515/1569397042722328 Fidaleo Francesco Dipartimento di Matematica, II Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy Infinite dimensional entangled Markov chains [Elektronische Daten] [Francesco Fidaleo] We continue the analysis of nontrivial examples of quantum Markov processes. This is done by applying the construction of entangled Markov chains obtained from classical Markov chains with infinite state-space. The formula giving the joint correlations arises from the corresponding classical formula by replacing the usual matrix multiplication by the Schur multiplication. In this way, we provide nontrivial examples of entangled Markov chains on , F being any infinite dimensional type I factor, J a finite interval of , and the bar the von Neumann tensor product between von Neumann algebras. We then have new nontrivial examples of quantum random walks which could play a rôle in quantum information theory. In view of applications to quantum statistical mechanics too, we see that the ergodic type of an entangled Markov chain is completely determined by the corresponding ergodic type of the underlying classical chain, provided that the latter admits an invariant probability distribution. This result parallels the corresponding one relative to the finite dimensional case. Finally, starting from random walks on discrete ICC groups, we exhibit examples of quantum Markov processes based on type II1 von Neumann factors. Copyright 2003, Walter de Gruyter Non commutative measure nationallicence integration and probability nationallicence Classifications of C∗- algebras nationallicence factors nationallicence Applications of selfadjoint operator algebras to physics nationallicence Quantum Markov processes nationallicence Quantum random walks nationallicence Quantum information theory nationallicence Random Operators and Stochastic Equations Walter de Gruyter 12/4(2004-12-01), 393-404 0926-6364 12:4<393 2004 12 rose https://doi.org/10.1515/1569397042722328 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569397042722328 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fidaleo Francesco Dipartimento di Matematica, II Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy NATIONALLICENCE 773 0- Random Operators and Stochastic Equations Walter de Gruyter 12/4(2004-12-01), 393-404 0926-6364 12:4<393 2004 12 rose CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter