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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 Tₗᵢₘ, we find that a noiseless amplifier with amplitude gain g can improve this value to Tₗᵢₘ/g², corresponding to an increase in distance proportional to logg.
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Blandino et al. (2012) studied this question.
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