  It is shown that the capacity of the channel modeled by (a discretized
version of) the stochastic nonlinear Schr\"odinger (NLS) equation is
upper-bounded by $\log(1+\text{SNR})$ with $\text{SNR}=\mathcal
P_0/\sigma^2(z)$, where $\mathcal P_0$ is the average input signal power and
$\sigma^2(z)$ is the total noise power up to distance $z$. The result is a
consequence of the fact that the deterministic NLS equation is a Hamiltonian
energy-preserving dynamical system.
