Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier

We show that the maximum transmission distance of continuous-variable quantum key distribution in presence of a Gaussian noisy lossy channel can be arbitrarily increased using a heralded noiseless linear amplifier. We explicitly consider a protocol using amplitude- and phase-modulated coherent states with reverse reconciliation. Assuming that the secret key rate drops to zero for a line transmittance T-lim, we find that a noiseless amplifier with amplitude gain g can improve this value to T-lim/g(2), corresponding to an increase in distance proportional to log g.