How Close to Maximum Entropy Is Amplified Coherent Light?

We analyze the issue of entropy maximization for discrete communication channels under both mean and variance constraints. The probability-distribution solution, ξ(k), is substantially different from that of amplified coherent light, φ(k), while the corresponding entropies H(ξ) and H(φ) are found to be very nearly equal. At high signals, both H(ξ) and H(φ) converge to the continuous-channel entropy given by Gaussian statistics. Amplified coherent light can thus be considered to be very close to entropy maximum, regardless of the signal level.