Error performance limit of binary quantum communications over a turbulent medium

In this paper we consider the detection of noisy binary quantum optical coherent states transmitted over a turbulent medium, such as terrestrial links or satellite optical connections across the atmosphere. The propagation effect is accounted for by a random attenuation factor, which is characterized in terms of its statistical distribution. Depending on the knowledge of the propagation coefficient, error performance can vary significantly and different receiver structures show different behaviors and robustness to the channel mismatch. The performance of the quantum optimal receiver and the square root measurement (SRM) are compared, and their sensitivity to the variability of the propagation coefficient is considered. It results that the phase variability of the propagation coefficient plays a fundamental role. The optimal receiver, in the absence of instantaneous channel knowledge, performs worse than the SRM, denoting a greater sensitivity to channel estimation accuracy.