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In this work we study the use of noiseless attenuation and noiseless amplification, in terms of multi-mode Continuous-Variable (CV) Quantum Key Distribution (QKD) over satellite-to-ground channels. We propose an improved multi-mode CV-QKD protocol where noiseless attenuation and noiseless amplification operations are applied at the transmitter and the receiver, respectively. Our results show that consistent with single-mode CV-QKD, the noiseless amplification operation, when applied at the receiver, can increase the transmission distance and the channel noise tolerance of multi-mode CV-QKD. Different from single-mode CV-QKD, in multi-mode CV-QKD the key rate improvement offered by noiseless amplification can be further enhanced by adding noiseless attenuation at the transmitter.

Multi-mode CV-QKD with Noiseless Attenuation and Amplification