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In the literature the performance of quantum data transmission systems isusually evaluated in the absence of thermal noise. A more realistic approachtaking into account the thermal noise is intrinsically more difficult becauseit requires dealing with Glauber coherent states in an infinite--dimensionalspace. In particular, the exact evaluation of the optimal measurement operatorsis a very difficult task, and numerical approximation is unavoidable. The paperfaces the problem by approximating the P-representation of the noisy quantumstates with a large but finite number of terms and applying to them the squareroot measurement (SRM) approach. Comparisons with the exact solution obtainedwith convex semidefinite programming show that the SRM approach gives quiteaccurate results. As application, the performance of quadrature amplitudemodulation (QAM) and phase shift keying (PSK) systems is considered. In spiteof the fact that the SRM approach is not optimal and overestimates the errorprobability, also in these cases the quantum detection maintains itssuperiority with respect to the classical homodyne detection.

Performance of quantum data transmission systems in the presence of thermal noise