  We address the estimation of the loss parameter of a bosonic channel probed
by Gaussian signals. We derive the ultimate quantum bound on precision and show
that no improvement may be obtained by having access to the environment degrees
of freedom. We found that, for small losses, the variance of the optimal
estimator is proportional to the loss parameter itself, a result that
represents a qualitative improvement over the shot noise limit. An observable
based on the symmetric logarithmic derivative is derived, which attains the
ultimate bound and may be implemented using Gaussian operations and photon
counting.
