  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.
