Repeated Quantum Interactions and Unitary Random Walks

Stéphane Attal (1) , Ameur Dhahri (2)

1 ICJ - Institut Camille Jordan
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in $\RR^N$. The characterization we obtain is entirely algebraical in terms of the unitary operator driving the elementary interaction. We show that the solutions of these equations are then random walks on the group $U(\rH_0)$ of unitary operators on $\rH_0$.

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]

Stéphane Attal, Ameur Dhahri. Repeated Quantum Interactions and Unitary Random Walks. Journal of Theoretical Probability, 2010, 23, pp.345-361. ⟨hal-00199955⟩