  We study the propagation of quantum states of light in separable
longitudinally inhomogeneous media. By means of the usual quantization approach
this kind of media would lead to the unphysical result of quantum noise
squeezing. This problem is solved by means of generalized canonical
transformations in a comoving frame. Under these transformations the generator
of propagation is a physical Lewis-Ermakov invariant in space which is
quantized and, accordingly, a propagator consistent with experiments is
obtained. Finally, we show that the net effect produced by propagation in these
media is a quantum Gouy's phase with application in quantum interferometry.
