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 toward 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.

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