Satellite-to-Ground Continuous Variable Quantum Key Distribution: The Gaussian and Discrete Modulated 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 quantum key distribution (QKD). An alternative modulation scheme is the discrete modulated CVQKD (DM-CVQKD) protocol. In this paper, we perform a feasibility study for practical satellite-to-ground CVQKD with a focus on comparing existing GM-CVQKD and DM-CVQKD protocols with the application of the performance of recent reconciliation methods. We use a satellite-to-ground link model which takes into account geometric losses, 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. Realistic parameters have been used for the calculation of the secret key rate (SKR) along with a comparison between MD and MLC-MSD reconciliation during satellite-to-ground GM-CVQKD, for the first time. The results show that GM-CVQKD outperforms DM-CVQKD. In addition, GM-CVQKD with MD reconciliation outperforms GM-CVQKD with MLC-MSD reconciliation in the finite size limit by producing positive SKRs at larger link distances and lower elevation angles.