Improve the Maximum Transmission Distance of Four-State Continuous Variable Quantum Key Distribution by using a Noiseless Linear Amplifier

A modified four-state CVQKD protocol is proposed to increase the maximum transmission distance and tolerable excess noise in the presence of Gaussian lossy and noisy channel by using a noiseless linear amplifier (NLA). A NLA with amplitude gain g canincrease the maximum admission losses by 20log(g) dB.