Homodyne detection for atmosphere channels
  We give a systematic theoretical description of homodyne detection in the case where both the signal and the local oscillator pass through the turbulent atmosphere. Imperfect knowledge of the local-oscillator amplitude is effectively included in a noisy density operator, leading to postprocessing noise. Alternatively, we propose a technique with monitored transmission coefficient of the atmosphere, which is free of postprocessing noise. 
A. A. Semenov, F. T\"oppel, D. Yu. Vasylyev, H. V. Gomonay, W. Vogel
quant-ph