  We 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.
