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

Developing quantum key distribution (QKD) protocols resistant to losses and noises is of great importance in practice. We show that the maximum transmission distance and tolerable excess noise of the Gaussian modulation (GM) and discrete modulation (DM) CVQKD protocols can be dramatically increased by using a noiseless linear amplifier (NLA). It is proved that a NLA with gain g can increase the maximum transmission distance by 20 /αlog₁₀ g km, where a = 0.2 dB/km is the loss coefficient of the fiber channel.