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arXiv:2608.20088

Squeezed- and coherent-state quantum key distribution over a deployed hybrid fibre-free-space channel

Adnan A. E. Hajomer, Huy Q. Nguyen, Ivan Derkach, Andreas B. Kidmose, Edoardo Rossi, Mattia Sabatini, Yoann Pietri, Marco Avesani, Francesco Vedovato, Michael Hentschel, Radim Filip, Giuseppe Vallone, Vladyslav Usenko, Tobias Gehring, Soren Forchhammer, Paolo Villoresi, Ulrik L. Andersen

quant-phSubmitted Aug 20, 2026• Announced Aug 21, 2026• 0 citations• Revised Aug 23, 2026 (v2)
v1 · Aug 20, 2026v2 · Aug 23, 2026
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Abstract

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.

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•Oct 21, 2025•0 citations
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.
Abstract Quantum key distribution (QKD) provides secure communication using quantum mechanics, with continuous-variable QKD (CV-QKD) being an attractive solution due to its compatibility with existing telecommunication technology. Its main drawback is susceptibility to signal loss in fibres and free-space links, including satellites, which limits performance. Here we show a software-based protocol enhancing CV-QKD by applying adaptive filters at the transmitter and receiver, allowing the system to dynamically respond to changing channel conditions. Our security analysis avoids relying on Gaussian extremality, giving accurate bounds on an eavesdropper’s information. The protocol can also extract keys in regions that would normally be considered insecure. We demonstrate a threefold increase in secret-key rates compared with the best existing CV-QKD protocol, and in satellite simulations, up to a 400-fold improvement. Because it requires no hardware modifications, our method can be readily integrated into existing systems, paving the way for more practical and robust quantum communication networks.
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%.
Future quantum communication infrastructures will need to serve heterogeneous users on shared physical channels: short-range, high-throughput links favor Continuous-Variable Quantum Key Distribution (CV-QKD), while long-reach, high-loss links remain the domain of Discrete-Variable QKD (DV-QKD). Wavelength-division multiplexing (WDM) of the two protocols on a common channel would address both regimes simultaneously, but their markedly different noise sensitivities make coexistence non-trivial and, to date, experimentally untested. Here we report the first simultaneous operation of two independent CV- and DV-QKD systems on a common optical channel, using standard C-band DWDM filters at 1550.12 nm (CV) and 1545.32 nm (DV). We demonstrate joint operation on both optical fiber and a 620 m urban daylight free-space link. On fiber, the two systems exhibit the expected complementarity, crossing over at 7.56 dB of channel loss where both deliver $\sim$1.43 Mbit/s; in daylight free-space, both sustain Mbit/s key rates under time-varying atmospheric attenuation. Across all configurations we observe no measurable multiplexing-induced penalty in QBER or excess noise. These results establish hybrid CV-DV WDM as a practical building block for heterogeneous quantum communication networks, where metropolitan high-throughput users and long-reach backbone links can be served on a single physical infrastructure.
Quadrature Phase Shift Keying Continuous Variable Quantum Key Distribution (QPSK CV-QKD) can be used to encode bits of information on weak coherent states, enhanced with quantum scissors. In our experiment, we use discretely modulated QPSK CV-QKD across a 150 m long Free-Space Optical (FSO) link over the two buildings with a four-symbol constellation. Other CV-QKD deployments in the literature have demonstrated a Frame Error Rate of 20% with a 100 MHz repetition rate and a loss of 6 dB in the channel. Our setup has a QBER of 25% for a 35 dB channel loss. Our system has been tested for a link loss of upto 50 dB. The QPSK symbols generated at 100 MHz from a Zynq Ultrascale+ Field Programmable Gated Array and fed to an I/Q transmitter, which in turn modulated a 1550 nm laser. The FSO transmitter, connected to our lab 500 m away, consists of a collimator and a beam expander. The transmitted states were captured on the other side by a FSO receiver unit consisting of a collimator. The received signal was transported back to the lab via a fiber of length 1 km, which is then passed through a 90 degree hybrid coherent receiver, with a 1 GHz bandwidth. The captured quadratures are post processed with a k-means cluster algorithm allowing us to recover the bit values. Our experiments focus on understanding the change in BER in the presence of varying levels of attenuation over the hybrid FSO+fibre channel.
Quantum key distribution (QKD) guarantees information-theoretic security by the laws of physics, but deployment at scale requires compact, manufacturable photonic terminals. Continuous-variable QKD (CV-QKD) is well suited for this transition through telecom-compatible, room-temperature coherent detection. However, unifying full on-chip core terminal integration, room-temperature operation, high loss tolerance, and composable end-to-end security in long-distance QKD remains a key bottleneck. Here we report a fully integrated CV-QKD platform in which two hybrid III--V/Si3_33​N4_44​ integrated lasers, a silicon transmitter, and a silicon coherent receiver implement the core terminal functions, operating with a local local oscillator (LLO) over fibre links of 25--150 km. A Bayesian machine-learning algorithm maintains robust phase lock throughout the long records required for composable security, consistently outperforming the conventional unscented Kalman filter, while rate-matched multidimensional reconciliation approaches the Shannon limit. The system certifies a composable finite-size secret-key rate of 29.3 kbps at 100 km from a 140-billion-symbol block, with 12.9 kbps at 125 km under finite-size analysis and 9.17 kbps at 150 km under asymptotic analysis. By establishing the longest finite-size and asymptotic reaches and the highest secret-key rate per symbol reported for integrated CV-QKD, this work advances the development of practical chip-based quantum networks.
The aim of this thesis is to develop continuous variable quantum key distribution (CVQKD) for the goal of securing a global quantum network. A numerical tool was developed for comparing different CVQKD protocols and identifying parameter spaces for positive and negative secret key rate (SKR) while taking into account the simultaneous effects of CVQKD parameters. Using the transmittance, excess noise, and amplitude modulation, the tool shows that the M-QAM protocol outperforms M-APSK which outperforms M-PSK. In addition, increasing the number of coherent states for a protocol non-linearly increases the capability of a protocol to produce positive SKRs. The tool also identifies parameters spaces, such as small excess noise regimes, where protocols have the same performance. The tool helps identify appropriate protocols for channels where parameters such as the transmittance and excess noise fluctuate, and can be extended to include more CVQKD parameters. The improvement of CVQKD in turbulent channels, through the use of adaptive optics (AO), was studied by investigating the interferometric visibility between a quantum signal and a local local oscillator in turbulent channels. The results showed that the adaptive optics system was able to increase the interferometric visibility and decrease its fluctuations. In the context of free-space CVQKD, these lead to larger positive and more precise SKRs. The structures of existing QKD networks were analysed and shown how they can be fit into a general three-layer QKD network architecture for the endeavour of a global QKD network architecture. The asymptotic and finite size limit SKRs were calculated for different links CVQKD can be used. The results show that CVQKD achieves longer distances in inter-satellite, satellite-to-ground, fibre, and underwater links in order. In addition, the Gaussian modulated (GM) CVQKD protocol with multidimensional (MD) reconciliation outperforms all other protocols studied by producing positive SKRs for longer link distances. The link capacity, a routing metric for secret key distribution, which considers a dynamic SKR based on dynamic links was developed. Its feasibility in simulated CVQKD networks was presented for the aim of spatiotemporal secret key distribution through a CVQKD network.