Relativistic Doppler effect in quantum communication

When an electromagnetic signal propagates in vacuo, a polarization detector cannot be rigorously perpendicular to the wave-vector because of diffraction effects. The vacuum behaves as a noisy channel, even if the detectors are perfect. The 'noise' can, however, be reduced and nearly cancelled by a relative motion of the observer towards the source. The standard definition of a reduced density matrix fails for photon polarization, because the transversality condition behaves like a superselection rule. We can, however, define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits and no exactly orthogonal qubit states.