  Since the invention of the laser in the 60s, one of the most fundamental
communication channels has been the free-space optical channel. For this type
of channel, a number of effects generally need to be considered, including
diffraction, refraction, atmospheric extinction, pointing errors and, most
importantly, turbulence. Because of all these adverse features, the free-space
optical (FSO) channel is more difficult to study than a stable fiber-based
link. For the same reasons, only recently it has been possible to establish the
ultimate performances achievable in quantum communications via free-space
channels, together with practical rates for continuous variable (CV) quantum
key distribution (QKD). Differently from previous literature, mainly focused on
the regime of weak turbulence, this work considers the FSO channel in the more
challenging regime of moderate-to-strong turbulence, where effects of beam
widening and breaking are more important than beam wandering. This regime may
occur in long-distance free-space links on the ground, in uplink to
high-altitude platform systems (HAPS) and, more interestingly, in downlink from
near-horizon satellites. In such a regime we rigorously investigate ultimate
limits for quantum communications and show that composable keys can be
extracted using CV-QKD.
