We analyze and compare the characterization of a quantum device in ter
ms of noise, transmitted bit-error-rate (BER) and mutual information,
showing how the noise description is meaningful only for Gaussian chan
nels. After reviewing the description of a quantum communication chann
el, we study the insertion of an amplifier. We focus attention on the
case of direct detection, where the linear amplifier has a 3 decibels
noise-figure, which is usually considered an unsurpassable limit, refe
rred to as the standard quantum limit (SQL). Both noise and BER could
be reduced using an ideal amplifier, which is feasible in principle. H
owever, just a reduction of noise beyond the SQL does not generally co
rrespond to an improvement of the BER or of the mutual information. Th
is is the case of a laser amplifier, where saturation can greatly redu
ce the noise-figure, although there is no corresponding improvement of
the BER. Such mechanism is illustrated on the basis of Monte Carlo si
mulations.