Driving non-Gaussian to Gaussian states with linear optics

We introduce a protocol that maps finite-dimensional pure input states onto approximately Gaussian states in an iterative procedure. This protocol can be used to distill highly entangled bi-partite Gaussian states from a supply of weakly entangled pure Gaussian states. The entire procedure requires only the use of passive optical elements and photon detectors that solely distinguish between the presence and absence of photons.