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

The Gaussian modulated continuous variable quantum key distribution (GM-CVQKD) protocol is known to maximise the mutual information between two parties during QKD. However, the reconciliation efficiency significantly decreases in low signal-to-noise ratio (SNR) regimes. In contrast, the more resilient discrete modulated CVQKD (DM-CVQKD) protocol has better reconciliation efficiencies in low SNR regimes. In this paper, we study the Phase Shift Keying (M-PSK) and Quadrature Amplitude Modulation (M-QAM) DM-CVQKD protocols along with the GM-CVQKD protocol over a satellite-to-ground link in the low SNR regime. We use a satellite-to-ground link model which takes into account geometric, scintillation, and scattering losses from the link distance, atmospheric turbulence, and atmospheric aerosols, respectively. In addition, recent multidimensional (MD) and multilevel coding and multistage decoding (MLC-MSD) reconciliation method models in combination with multiedge-type low-density parity-check (MET-LDPC) code models have been used to determine the reconciliation efficiency. The results show that the 4-PSK and 8-PSK protocols outperform GM-CVQKD in both the asymptotic and finite size limit of collective attacks by producing positive key rates at larger link distances and lower elevation angles when the SNR is low. In addition, the M-QAM protocol produces larger positive secret key rates compared to M-PSK in the asymptotic limit.