A certain class of mixed states artificially constructed that is used in quantum cryptography is crucial for representation of signals. This correspondence shows that the square-root measurement gives the optimal measurement for such a class of mixed states.

We analyze the performance of the error probability and the mutual information for quadrature amplitude modulation (QAM) and phase-shift keying systems based on quantum detection theory. It is shown that the quantum receiver called square root measurement gives about 5.7 dB improvement in power in comparison with the classical one. Furthermore, we show that the quantum QAM system can achieve the same reliability as the conventional intensity modulation-direct detection (IM-DD) system with almost equal power, compressing the required bandwidth, while the reliability is degraded in general.

From a general optical channel model, it is shown that the coupling loss intensity noise generated at connections of optical channels is caused by amplitude vector rotation and its dependency upon the coupling coefficient. The shape of the polarization is not important. This noise becomes muitiplicative noise so that the noise disturbs signals directly even if fluctuations of rotation of the amplitude vector are of low frequency. Detailed spectral properties and SNR are given for this type of noise, and the existence of a lower bound of SNR is shown. The coupling loss intensity noise becomes serious in the coupling of fibers and optical circuits, while it will not be important for the splicing of fibers.