Error probability in polarization sensitive communication systems in terms of moments of the channel’s rotation angle

Polarization effects of channels such as turbulent free space and optical fibers can deteriorate the quality of polarization-sensitive communication schemes, for example, quantum key distribution. The exact nature of the channel is problematic to determine, and most theoretical results are based on approximations. We introduce a general model with probabilistic polarization angle rotation and analyze the average error it causes in terms of the moments of the probability distribution. For a small rotation angle variance, an inequality between distributions’ errors is considered based on their kurtosis values and potentially higher-order central moments. An upper bound is determined for the error probability, holding for all practically interesting scenarios.