Open Quantum Random Walks: reducibility, period, ergodic properties

Raffaella Carbone (1) , Yan Pautrat (2)

1 UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We study the analogues of irreducibility, period, and communicating classes for open quantum random walks, as defined by Attal et al. (J. Stat. Phys., 2012). We recover results similar to the standard ones for Markov chains, in terms of ergodic behavior, decomposition into irreducible subsystems, and characterization of stationary states.

Mots clés: open quantum random walks; non-commutative Perron-Frobenius theorem; irreducible restrictions; period; invariant states

Domaines: Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Raffaella Carbone, Yan Pautrat. Open Quantum Random Walks: reducibility, period, ergodic properties. Annales Henri Poincaré, 2016, ⟨10.1007/s00023-015-0396-y⟩. ⟨hal-00990757⟩