2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220698We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.19 pagesMathematical PhysicsOperator AlgebrasQuantum Physics47A13, 46L53, 47A48, 47A40, 81R15text