Random repeated quantum interactions and random invariant states

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 asymptotic induced ensemble.