Optimized quantum-optical communications in the presence of loss

We consider the effect of loss on quantum-optical communication channels. The channel based on direct detection of number states, which for a lossless transmission line would achieve the ultimate quantum channel capacity, is easily degraded by loss. The same holds true for the channel based on homodyne detection of squeezed states, which also is very fragile to loss. On the contrary, the ``classical'' channel based on heterodyne detection of coherent states is loss-invariant. We optimize the a priori probability for the squeezed-state and the number-state channels, taking the effect of loss into account. In the low power regime we achieve a sizeable improvement of the mutual information, and both the squeezed-state and the number-state channels overcome the capacity of the coherent-state channel. In particular, the squeezed-state channel beats the classical channel for total average number of photons $N<8$. However, for sufficiently high power the classical channel always performs as the best one. For the number-state channel we show that with a loss $\eta\lesssim .6$ the optimized a priori probability departs from the usual thermal-like behavior, and develops gaps of zero probability, with a considerable improvement of the mutual information (up to 70 % of improvement at low power for attenuation $\eta=.15$).