  We study a class of optical circuits with vacuum input states consisting of
Gaussian sources without coherent displacements such as down-converters and
squeezers, together with detectors and passive interferometry (beam-splitters,
polarisation rotations, phase-shifters etc.). We show that the outgoing state
leaving the optical circuit can be expressed in terms of so-called
multi-dimensional Hermite polynomials and give their recursion and
orthogonality relations. We show how quantum teleportation of photon
polarisation can be modelled using this description.
