  The study of free-space quantum communications requires tools from quantum
information theory, optics and turbulence theory. Here we combine these tools
to bound the ultimate rates for key and entanglement distribution through a
free-space link, where the propagation of quantum systems is generally affected
by diffraction, atmospheric extinction, turbulence, pointing errors, and
background noise. Besides establishing ultimate limits, we also show that the
composable secret-key rate achievable by a suitable (pilot-guided and
post-selected) coherent-state protocol is sufficiently close to these limits,
therefore showing the suitability of free-space channels for high-rate quantum
key distribution. Our work provides analytical tools for assessing the
composable finite-size security of coherent-state protocols in general
conditions, from the standard assumption of a stable communication channel (as
is typical in fiber-based connections) to the more challenging scenario of a
fading channel (as is typical in free-space links).
