  We analyze the effect of phase fluctuations in an optical communication
scheme based on collective detection of sequences of binary coherent state
symbols using linear optics and photon counting. When the phase noise is
absent, the scheme offers qualitatively improved nonlinear scaling of the
spectral efficiency with the mean photon number in the low-power regime
compared to individual detection. We show that this feature, providing a
demonstration of superaddivitity of accessible information in classical
communication over quantum channels, is preserved if random phases imprinted on
transmitted symbols fluctuate around a reference fixed over the sequence
length.
