Real global-scale quantum communications and quantum key distribution systems cannot beimplemented 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 solution can be applied to fix the polarization errors which are critical in space-earth quantum communication systems. The channel coding scheme provides capacity-achieving communication over slightly depolarizing space-earth channels.correct the unknown errors of the channel, without any knowledge of the channel output pilot states. The probabilistic behavior of these controlled quantum gates, and the storing process of unitary transformations in quantum states were studied in the literature [12,13].An immediate practical application of the pilot quantum-error correction is in polarization compensation in space-earth quantum communications [1], [6], [14][15][16]. In space-earth quantum communications 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. The proposed quantum error-correction scheme can be applied to fix the polarization errors which are critical in space-earth quantum communication systems. Our polarization compensation scheme can be implemented in practice without any extra hardware or software costs, providing an easily implemented on-the-fly polarization compensation scheme. There are several polarization techniques existing in the literature, but in each case, further hardware and software implementations are required and the cost of these practical polarization solutions is high. Our scheme uses minimal redundancy and adds it into an arbitrary large block set instead of each individual qubits. Using our scheme, the error-correction of the data qubits can be achieved without any knowledge about angle of the polarization rotation error.This paper is organized as follows. In Section 2, we give an exact problem in space-earth quantum channels where the proposed technique can be applied. In Section 3 we show the details of the channel coding scheme. In Section 4 we introduce the channel model and express the capacities. In Section 5 we present t...