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arXiv:2408.12522 · Journal of Lightwave Technology

Rate-Adaptive Reconciliation for Experimental Continuous-Variable Quantum Key Distribution With Discrete Modulation Over a Free-Space Optical Link

Kadir Gümüş, João Frazão, Vincent van Vliet, Sjoerd van der Heide, Menno van den Hout, Gabriele Liga, Yunus Can Gültekin, Aaron Albores-Mejía, Thomas D. Bradley, Alex Alvarado, Chigo M. Okonkwo

Published Jan 15, 2025• 6 citations
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Abstract

Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use of$d$-dimensional reconciliation with$d > 8$to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%.

DOI
10.1109/jlt.2025.3530005

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Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use ofddd-dimensional reconciliation withd>8d > 8d>8to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%.
In free-space continuous-variable quantum key distribution (CV-QKD) systems, atmospheric turbulence induces time-varying fading, leading to random fluctuations in the signal-to-noise ratio (SNR). Consequently, rate-adaptive reconciliation becomes essential. This paper proposes a rate-adaptive high-dimensional reconciliation method based on Raptor-like LDPC codes. The proposed scheme achieves dynamic rate adaptation by leveraging a precomputed SNR threshold table. Furthermore, before adjusting the code length, the proposed method sorts high-dimensional vector blocks based on their norms, preferentially retaining blocks with higher signal power to bolster information reliability. Simulation results demonstrate that the proposed scheme outperforms the perforation and shortening (PS) method in terms of reconciliation efficiency and frame error rate, while maintaining decoding iterations below 100. Under random transmission rate samples, the optimized scheme achieves optimal secret key rate (SKR) performance and stability, validating its robustness and practicality in time-varying channels.
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.
This letter investigates a continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian-modulated coherent states over unmanned aerial vehicle (UAV)-based free-space optical (FSO) links. A realistic fading channel model is developed, including atmospheric turbulence, extinction, and UAV-induced pointing errors. We perform distance-dependent modulation variance optimization to maximize the secret key rate (SKR) under three scenarios: asymptotic, finite-block size (FBS), and FBS with adaptive optics (AO), based on numerical simulations incorporating a realistic UAV-FSO channel model. The results show that finite-size effects reduce the secure transmission range to ~800 m, while AO extends it to ~930 m. Furthermore, optimal modulation improves key rates by up to 40% compared to fixed modulation. This is the first work to jointly model UAV-FSO channel fluctuations, optimize modulation, and quantify finite-size security with AO, confirming the feasibility of CV-QKD for UAV-based communications.
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Quantum networks will combine optical fibre with free-space links, yet continuous-variable quantum key distribution (CV-QKD) has been developed predominantly for one medium or the other, while operation across concatenated fibre-free-space channels remains largely unexplored. The two media impose contrasting requirements: fibre transmission is stable and permits long processing intervals, whereas atmospheric propagation imposes transmittance fluctuations that degrade security and must be resolved on short timescales. Here we demonstrate a locally generated local oscillator CV-QKD with both Gaussian-modulated coherent and squeezed states over a deployed hybrid channel comprising a 620-m free-space link and 2 km of deployed fibre, with a total loss up to 20 dB. Rather than adapting the optics to each medium, we move channel adaptation to the post-processing, through a unified adaptive post-processing framework coupling transmittance-based clustering, residual-fading mitigation by covariance-matrix averaging or de-fading, and rate-adaptive blind reconciliation, which alone recovers up to 19% additional key. The same adaptive-processing principle is applied to both protocols, while accounting for their different security analyses and statistical requirements, yielding asymptotic secret-key rates of 0.42 Mbit per sec for the coherent-state protocol and 0.93 Mbit per sec for the squeezed-state protocol under the respective channel conditions, and establishing squeezed-state CV-QKD over a deployed atmospheric channel. These results show that adaptation to the transmission medium can largely be transferred to the data-processing layer, providing a route towards heterogeneous quantum networks spanning fibre, terrestrial free-space and satellite links.