  Real global-scale quantum communications and quantum key distribution systems
cannot be implemented by the current fiber and free-space links. These links
have high attenuation, low polarization-preserving capability or extreme
sensitivity to the environment. A potential solution to the problem is the
space-earth quantum channels. These channels have no absorption since the
signal states are propagated in empty space, however a small fraction of these
channels is in the atmosphere, which causes slight depolarizing effect.
Furthermore, the relative motion of the ground station and the satellite causes
a rotation in the polarization of the quantum states. In the current approaches
to compensate for these types of polarization errors, high computational costs
and extra physical apparatuses are required. Here we introduce a novel approach
which breaks with the traditional views of currently developed quantum-error
correction schemes. The proposed quantum error-correction technique can be
applied to fix the polarization errors which are critical in space-earth
quantum communication systems. Moreover, the channel coding scheme provides
capacity-achieving communication over slightly depolarizing space-earth
channels.
