  To achieve the maximum information transfer and face a possible eavesdropper,
the samples transmitted in continuous-variable quantum key distribution
(CV-QKD) protocols are to be drawn from a continuous Gaussian distribution. As
a matter of fact, in practical implementations the transmitter has a finite
(power) dynamics and the Gaussian sampling can be only approximated. This
requires the quantum protocols to operate at small powers. In this paper, we
show that a suitable probabilistic amplitude shaping of a finite set of symbols
allows to approximate at will the optimal channel capacity also for increasing
average powers. We investigate the feasibility of this approach in the
framework of CV-QKD, propose a protocol employing discrete quadrature amplitude
modulation assisted with probabilistic amplitude shaping, and we perform the
key generation rate analysis assuming a wiretap channel and lossless homodyne
detection.
