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The Gaussian modulated continuous variable quantum key distribution(GM-CVQKD) protocol is known to maximise the mutual information between twoparties during quantum key distribution (QKD). An alternative modulation schemeis the discrete modulated CVQKD (DM-CVQKD) protocol. In this paper, we studythe Phase Shift Keying (M-PSK) and Quadrature Amplitude Modulation (M QAM)DM-CVQKD protocols along with the GM-CVQKD protocol over a satellite-to-groundlink in the low SNR regime. We use a satellite-to-ground link model which takesinto account geometric losses, scintillation, and scattering losses from thelink distance, atmospheric turbulence, and atmospheric aerosols, respectively.In addition, recent multidimensional (MD) and multilevel coding and multistagedecoding (MLC-MSD) reconciliation method models in combination withmultiedge-type low-density parity-check (MET-LDPC) code models have been usedto determine the reconciliation efficiency. The results show that GM-CVQKDoutperforms DM-CVQKD. In addition, GM-CVQKD with MD reconciliation outperformsGM-CVQKD with MLC-MSD reconciliation in the finite size limit by producingpositive secret key rates at larger link distances and lower elevation angles.

Satellite-to-Ground Continuous Variable Quantum Key Distribution: The Gaussian and Discrete Modulated Protocols in Low Earth Orbit