  Multi-level quantum protocols may potentially supersede standard quantum
optical polarization-encoded protocols in terms of amount of information
transmission and security. However, for free space telecomunications, we do not
have tools for limiting loss due to diffraction and perturbations, as for
example turbulence in air. Here we study propagation invariant quantum X-waves
with angular momentum; this representation expresses the electromagnetic field
as a quantum gas of weakly interacting bosons. The resulting spatio-temporal
quantized light pulses are not subject to diffraction and dispersion, and are
intrinsically resilient to disturbances in propagation. We show that
spontaneous down-conversion generates squeezed X-waves useful for quantum
protocols. Surprisingly the orbital angural momentum affects the squeezing
angle, and we predict the existence of a characteristic axicon aperture for
maximal squeezing. There results may boost the applications in free space of
quantum optical transmission and multi-level quantum protocols, and may also be
relevant for novel kinds of interferometers, as satellite-based gravitational
wave detectors.
