Four-State Modulation in Middle of a Quantum Channel for Continuous-Variable Quantum Key Distribution Protocol with Noiseless Linear Amplifier

We characterize a modified continuous-variable quantum key distribution (CV-QKD) protocol with four states in the middle of a quantum channel. In this protocol, two noiseless linear amplifiers (NLAs) are inserted before each detector of the two parts, Alice and Bob, with the purpose of increasing the secret key rate and the maximum transmission distance. We present the performance analysis of the new four-state CV-QKD protocol over a Gaussian lossy and noisy channel. The simulation results show that the NLAs with a reasonable gain g can effectively enhance the secret key rate as well as the maximum transmission distance, which is generally satisfied in practice.