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 $\log g$.

• Received 14 May 2012

DOI:https://doi.org/10.1103/PhysRevA.86.012327