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Scientific Reports

Improving free-space continuous variable quantum key distribution with adaptive optics

Mikhael Sayat, Marcus Birch, Michael Copeland, Elisa Jager, Oliver Thearle, Francis Bennet, Ping Koy Lam, Nicholas James Rattenbury, John Edward Cater

Published Jan 24, 2026• 3 citations
Publisher

Abstract

A significant performance inhibitor of free-space continuous variable quantum key distribution (CVQKD) is turbulence, which gives rise to wavefront phase and amplitude aberrations. We demonstrate that in a turbulent channel, during coherent state transmissions from a continuous-wave laser, that the interferometric visibility between the local oscillator (LO) and quantum signal decreases. A solution to this is incorporating adaptive optics at the receiver to correct phase and amplitude aberrations in the wavefronts of the received quantum signal. We demonstrate the increased interferometric visibility and decrease in its fluctuations in a 60 cm and 30 m turbulent channel when using adaptive optics through channel characterisation. In an ideal CVQKD system, we show that this leads to more precise and larger positive secret key rates, improving the performance of free-space CVQKD in turbulent channels.

DOI
10.1038/s41598-026-36805-7

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A significant performance inhibitor of free-space continuous variable quantum key distribution (CVQKD) is turbulence, which gives rise to wavefront phase and amplitude aberrations. We demonstrate that in a turbulent channel, during coherent state transmissions from a continuous-wave laser, that the interferometric visibility between the local oscillator (LO) and quantum signal decreases. A solution to this is incorporating adaptive optics at the receiver to correct phase and amplitude aberrations in the wavefronts of the received quantum signal. We demonstrate the increased interferometric visibility and decrease in its fluctuations in a 60 cm and 30 m turbulent channel when using adaptive optics through channel characterisation. In an ideal CVQKD system, we show that this leads to more precise and larger positive secret key rates, improving the performance of free-space CVQKD in turbulent channels.
A significant performance inhibitor of free-space continuous variable quantum key distribution (CVQKD) is turbulence, which gives rise to wavefront phase and amplitude aberrations. We demonstrate that in a turbulent channel, during coherent state transmissions from a continuous-wave laser, that the interferometric visibility between the local oscillator (LO) and quantum signal decreases. A solution to this is incorporating adaptive optics at the receiver to correct phase and amplitude aberrations in the wavefronts of the received quantum signal. We demonstrate the increased interferometric visibility and decrease in its fluctuations in a 60 cm and 30 m turbulent channel when using adaptive optics through channel characterisation. In an ideal CVQKD system, we show that this leads to more precise and larger positive secret key rates, improving the performance of free-space CVQKD in turbulent channels.
Continuous variable quantum key distribution (CVQKD) is the sharing of a secret key between parties using the continuous quadratures of light, the phase and amplitude quadratures, which can infer the presence of an eavesdropper using fundamental quantum mechanics. A significant performance inhibitor of free-space CVQKD is turbulence which gives rise to optical wavefront distortions consisting of random phase and amplitude fluctuations (scintillation). In this work, we experimentally study the negative effects of turbulence on coherent states in a free-space channel for CVQKD. We demonstrate during coherent state transmissions from a continuous-wave laser in a turbulent channel, the interferometric visibility between a local oscillator and signal fluctuates and decreases with higher degrees of scintillation. This leads to the breaking of the phase-lock between the local oscillator and quantum signal and a decrease in the secret key rate (SKR). By incorporating an adaptive optics system, the degraded optical wavefront from turbulence can be corrected using a closed-feedback loop. This leads to the stabilisation and reduction in the decrease of the interferometric visibility in a turbulent channel. The improvement provided by adaptive optics leads to the increased performance of CVQKD, resulting in positive SKRs, which would have otherwise been infeasible in a turbulent channel.
Gaussian modulation of quantum coherent states are more adaptable with traditional optical communication equipment and have better compatibility with fiber channel in the spatial continuous variable quantum key distribution (CVQKD). We construct a spatial CVQKD model to analyze the effects of turbulent channel parameters, such as beam spreading, absorption, scattering and drift. The model innovatively introduces the role of the phase difference jitter between local oscillator (LO) and quantum signal light. The findings demonstrate a positive correlation between the excess noise and the transmission distance, turbulence intensity, and the time between the LO and the quantum signal light. The secret key rate decreases with the increase of delay time. The simulation results can provide a reference for the design and optimization of the actual spatial CVQKD system.
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.
Continuous variable quantum key distribution (CVQKD) has been implemented over the atmospheric channels over free space. However, atmospheric turbulence weakens the quality of the transmitting quantum signals and hence decreases the secret key rate of the system. Here, we suggest an atmospheric turbulence channel model that involves atmospheric turbulence bubbles and demonstrates the implementation feasibility of passive CVQKD with spectrum resources in the terahertz band over the atmospheric turbulence channel. We achieve the channel transmittance characterized by the refractive index and the wavefront distortions. Moreover, an adaptive optics (AO) unit is used for performance improvement while considering the effect of the thermal noise and excess noise on the atmospheric turbulence bubble-modeled channel. Numerical simulations show that the AO-involved detection scheme can result in reductions in excess noise when being faced with the floating clouds and mist in atmospheric turbulence, which results in performance improvements in terms of secret key rate, which confirms the utility of the high-rate and long-distance CVQKD in terahertz (THz) for practical implementations.
When undertaking continuous-variable quantum key distribution (CV-QKD) across atmospheric channels, strong classical local oscillators (LOs) are often polarization-multiplexed with the weak quantum signals for coherent measurement at the receiver. Although the wavefronts of the quantum signal and LO are often assumed to experience the same distortion across channels, previous theoretical work has shown that they can experience differential distortions, resulting in relative wavefront errors (WFEs). Such errors have previously been shown to limit CV-QKD performance, in some cases leading to zero secure key rates. In this work, for the first time, we provide strong experimental evidence that relative WFEs are present in some circumstances and that standard assumptions in CVQKD deployments may need to be revisited. In addition, we demonstrate how turbulence can affect the detailed form of the relative WFEs, thereby indicating that long-range links like terrestrial-satellite channels are likely impacted more than shortrange terrestrial-only channels.