  Continuous-variable quantum key distribution protocols, based on Gaussian
modulation of the quadratures of coherent states, have been implemented in
recent experiments. A present limitation of such systems is the finite
efficiency of the detectors, which can in principle be compensated for by the
use of classical optical preamplifiers. Here we study this possibility in
detail, by deriving the modified secret key generation rates when an optical
parametric amplifier is placed at the output of the quantum channel. After
presenting a general set of security proofs, we show that the use of
preamplifiers does compensate for all the imperfections of the detectors when
the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can
also enhance the system performance, under conditions which are generally
satisfied in practice.
