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Optics Communications

Finite-size secret key rate analysis of a discrete-modulated continuous-variable quantum key distribution protocol for satellite-to-ground fading channel

Chetan Waghmare, Ashwin Kothari

Published Jun 15, 2025• 2 citations
Publisher
DOI
10.1016/j.optcom.2025.132044

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The satellite-mediated continuous-variable quantum key distribution (CV-QKD) protocol, which relies on off-the-shelf telecommunication components, has the potential for a global quantum communication network with all-day operation. However, the transmittance fluctuation of satellite-mediated links leads to the arriving quantum state showing non-Gaussian property, introducing extra fading noise in security analysis and limiting the secret key rate of the protocol. Here, we consider the clusterization method for data post-processing to suppress the fading noise in both downlink and uplink scenarios, where the measurement data are divided into several clusters, and we perform security analysis separately. In particular, we set the optimal upper and lower bounds of each cluster in terms of the probability distribution of transmittance (PDT), while finding an optimal cluster number for the trade-off between fading noise and the composable finite-size effect. Numerical analysis shows that the proposed method can improve the composable finite-size rate when the fading noise is large enough, even with only two clusters. Moreover, a high-speed CV-QKD system with a higher frequency of signal preparation and detection can extend the proposed method to work in the case of lower fading noise.
We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.
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.