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Free-Space Continuous Variable Quantum Key Distribution: Towards a Global Quantum Network

Mikhael Sayat

Published Oct 21, 2025• 0 citations
OpenAlex

Abstract

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.

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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.
The standard way to measure the performance of existing continuous variable quantum key distribution (CVQKD) protocols is by using the achievable secret key rate (SKR) with respect to one parameter while keeping all other parameters constant. However, this atomistic method requires many individual parameter analyses while overlooking the co-dependence of other parameters. In this work, a numerical tool is developed for comparing different CVQKD protocols while taking into account the simultaneous effects of multiple CVQKD parameters on the capability of protocols to produce positive SKRs. Using the transmittance, excess noise, and modulation amplitude parameter space, regions of positive SKR are identified to compare three discrete modulated (DM) CVQKD protocols. The results show that the M-QAM protocol outperforms the M-APSK and M-PSK protocols and that there is a non-linear increase in the capability to produce positive SKRs as the number of coherent states used for a protocol increases. The tool developed is beneficial for choosing the optimum protocol in unstable channels, such as free space, where the transmittance and excess noise fluctuate, providing a more holistic assessment of a protocol’s capability to produce positive SKRs.
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) uses the continuous quadratures of light to share a secret key between a transmitter and receiver. The presence of an eavesdropper can be detected by fundamental quantum mechanics. Compared to the more established discrete variable QKD, CVQKD uses more cost-effective homodyne detectors which are more compatible with current telecommunication technologies. In a future global quantum network, CVQKD could be used to ensure the secure exchange of information. In this work, the feasibility of a variety of CVQKD protocols in different channels that could be used to establish a global quantum network are studied. These are the Gaussian modulated and discrete modulated CVQKD protocols for satellite to optical ground station downlinks and uplinks for Earth-space connections, inter-satellite links for space connections, satellite to ship and underwater links for maritime connections, and fibre network links for terrestrial connections. Secret key distribution between continents and various regions is simulated while accounting for the different adverse effects associated with each link. The combination of these connections with routing and scheduling ensures inter-continental high-speed information exchange with unconditional security that is required to achieve the goal of a global quantum network.
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.
Abstract Continuous variable quantum key distribution (CVQKD) is a developing method to secure information exchange in future quantum networks. With the recent developments in quantum technology and greater access to space, a global quantum network secured by CVQKD can be within reach. In this work, the structures of existing QKD networks are analyzed, and how they can be fit into a general overarching three‐layer QKD network architecture for the endeavor of a global QKD network. Such a network can comprise different links in fiber and free‐space. The finite size limit secret key rates (SKRs) with multidimensional reconciliation are calculated for the different links for which CVQKD can be used in such a network. The results show that CVQKD generally achieves longer distances and larger SKRs in inter‐satellite, satellite‐to‐ground, fiber, and underwater links in descending order. The different links and nodes are classified and secret key distribution is studied as a graph problem. The link capacity, a routing metric for secret key distribution, which considers a dynamic SKR based on dynamic links is presented. Its use in simulated CVQKD networks is presented for the aim of spatiotemporal secret key distribution through a dynamic CVQKD network.
Abstract Continuous variable quantum key distribution (CVQKD) is a developing method to secure information exchange in future quantum networks. With the recent developments in quantum technology and greater access to space, a global quantum network secured by CVQKD can be within reach. In this work, the structures of existing QKD networks are analyzed, and how they can be fit into a general overarching three‐layer QKD network architecture for the endeavor of a global QKD network. Such a network can comprise different links in fiber and free‐space. The finite size limit secret key rates (SKRs) with multidimensional reconciliation are calculated for the different links for which CVQKD can be used in such a network. The results show that CVQKD generally achieves longer distances and larger SKRs in inter‐satellite, satellite‐to‐ground, fiber, and underwater links in descending order. The different links and nodes are classified and secret key distribution is studied as a graph problem. The link capacity, a routing metric for secret key distribution, which considers a dynamic SKR based on dynamic links is presented. Its use in simulated CVQKD networks is presented for the aim of spatiotemporal secret key distribution through a dynamic CVQKD network.