Random repeated quantum interactions and random invariant states

Ion Nechita (1) , Clément Pellegrini (2)

1 ICJ - Institut Camille Jordan
2 School of Physics and National Institue for Theoretical Physics

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}.

Mots clés: Quantum repeated interactions; random quantum channels; random matrices; peripheral spectrum; random density matrices

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

Ion Nechita, Clément Pellegrini. Random repeated quantum interactions and random invariant states. 2009. ⟨hal-00361509⟩