  In this letter, we investigate the quantum optical properties of
driven-dissipative nonlinear systems in a cascade configuration. We show that
pumping a nonlinear system with a state having a noncoherent statistics, can
improve the antibunching of the output state and, consequently, the
nonclassicality of the whole system. Furthermore, we show that is possible to
generate entanglement through dissipative coupling. These results applies to a
broad category of physical systems with a Kerr-like non-linearity, from Rydberg
atoms to exciton polaritons in microcavities.
