Realistic performance of the maximum information channel

For a fixed mean signal energy, the optimal narrow-band bosonic channel is based on photodetection of a Bose-Einstein distribution of number states. A simple formula is obtained for the average error probability per symbol of this channel when degraded by Gaussian noise and inefficient detection. A general information bound is derived for narrow-band channels degraded by Gaussian noise, which yields a lower bound for the average probability of error per bit. Results are applicable to all number-state channels in the limit of low noise and high efficiency.