  Satellite quantum communications are emerging within the panorama of quantum
technologies as a more effective strategy to distribute completely-secure keys
at very long distances, therefore playing an important role in the architecture
of a large-scale quantum network. In this work, we apply and extend recent
results in free-space quantum communications to determine the ultimate limits
at which secret (and entanglement) bits can be distributed via satellites. Our
study is comprehensive of the various practical scenarios, encompassing both
downlink and uplink configurations, with satellites at different altitudes and
zenith angles. It includes effects of diffraction, extinction, background noise
and fading, due to pointing errors and atmospheric turbulence (appropriately
developed for slant distances). Besides identifying upper bounds, we also
discuss lower bounds, i.e., achievable rates for key generation and
entanglement distribution. In particular, we study the composable finite-size
secret key rates that are achievable by protocols of continuous variable
quantum key distribution, for both downlink and uplink, showing the feasibility
of this approach for all configurations. Finally, we present a study with a
sun-synchronous satellite, showing that its key distribution rate is able to
outperform a ground chain of ideal quantum repeaters.
