ABSTRACT Temporal dynamics of free‐space continuous‐variable quantum key distribution (CV‐QKD) are intrinsically complicated by atmospheric turbulence‐induced channel fluctuations. The finite‐state Markov (FSM) framework provides a promising approach for mapping temporal evolution into state transitions. However, its application to CV‐QKD remains challenging due to the need for accurate characterization of both channel statistics and temporal correlations. Here, we derive the joint probability density function (PDF) of channel transmittance and its time derivative for log‐normal (LN) and Gamma–Gamma (GG) turbulence models. Based on a spectral‐domain analytical (SDA) approach incorporating inner‐ and outer‐scale effects, we derive temporal channel parameters and quantify the impact of adaptive optics (AO). Furthermore, the level crossing rate (LCR) of channel loss is derived to construct state transition probabilities (STPs) for the FSM framework, which is then employed to predict the temporal evolution of channel transmittance and achievable secret key rate (SKR).Results demonstrate that the proposed FSM framework accurately captures temporal dynamics of free‐space CV‐QKD and turbulence‐induced fluctuations. Under weak turbulence, AO enhances temporal correlation, increases mean SKR, and suppresses short‐term SKR fluctuations. Under strong turbulence, AO improves mean SKR but provides limited enhancement of temporal correlation and fluctuation suppression due to physical constraints.
ABSTRACT Temporal dynamics of free‐space continuous‐variable quantum key distribution (CV‐QKD) are intrinsically complicated by atmospheric turbulence‐induced channel fluctuations. The finite‐state Markov (FSM) framework provides a promising approach for mapping temporal evolution into state transitions. However, its application to CV‐QKD remains challenging due to the need for accurate characterization of both channel statistics and temporal correlations. Here, we derive the joint probability density function (PDF) of channel transmittance and its time derivative for log‐normal (LN) and Gamma–Gamma (GG) turbulence models. Based on a spectral‐domain analytical (SDA) approach incorporating inner‐ and outer‐scale effects, we derive temporal channel parameters and quantify the impact of adaptive optics (AO). Furthermore, the level crossing rate (LCR) of channel loss is derived to construct state transition probabilities (STPs) for the FSM framework, which is then employed to predict the temporal evolution of channel transmittance and achievable secret key rate (SKR).Results demonstrate that the proposed FSM framework accurately captures temporal dynamics of free‐space CV‐QKD and turbulence‐induced fluctuations. Under weak turbulence, AO enhances temporal correlation, increases mean SKR, and suppresses short‐term SKR fluctuations. Under strong turbulence, AO improves mean SKR but provides limited enhancement of temporal correlation and fluctuation suppression due to physical constraints.
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.
Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.
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.
We propose and experimentally investigate a high-speed Kramers-Kronig (KK) scheme based continuous-variable quantum key distribution (CV-QKD) system over a free-space optical (FSO) channel. The atmospheric turbulence channel is emulated by three spatial light modulators on which three randomly generated azimuthal phase patterns yielding Andrews' spectrum are recorded. The proposed KK scheme enables a low-complexity implementation, insensitivity to laser phase noise, low detection noise, and accurate channel transmittance monitoring. In addition, eight state CV-QKD protocols and 10-channels wavelength-division multiplexing (WDM) scheme are experimentally verified to obtain a high secure key rate. In our experiment, the minimum transmittance of 0.6 is required to guarantee the secure transmission, and a total SKR of 2.1 Gb/s can be obtained at the mean transmittance in weak turbulence regime.
The advent of quantum computers has significantly challenged the security of traditional cryptographic systems, prompting a surge in research on quantum key distribution (QKD). Among various QKD approaches, continuous-variable QKD (CVQKD) offers superior resilience against background noise. However, the local local oscillator (LLO) CVQKD scheme faces substantial physical limitations in scenarios with high channel attenuation, and the large attenuation CVQKD remains unrealized. Bottleneck challenges include ensuring stable low-noise transmission and accurately estimating parameters under fluctuating channel conditions. We propose a continuous-mode theoretical framework that provides an analytical method for time-varying quantum systems within a free-space channel. This framework can achieve high-fidelity LLO-CVQKD in free space without the need for complex, real-time frequency locking and transmittance calibration equipment. It can also enable free-space QKD under large attenuation and high repetition frequency. Through experimental validation, we first demonstrate high-rate secure quantum key distribution over high-loss free-space channels. Specifically, we achieve asymptotic key rates of 76.366 kbps and 403.896 kbps in 25 dB attenuation free-space channels without turbulence and 21.5 dB average attenuation free-space channels with turbulence, respectively. Additionally, we confirm the feasibility of experiments on mildly turbulent atmospheric channels spanning at least 10.5 km using current equipment. Our scheme provides direct insight into constructing an integrated air-ground quantum communication network.
Satellite-based Quantum Key Distribution (QKD) has emerged as a promising solution for global secure communication beyond the limitations of terrestrial optical fiber networks. However, practical free-space optical (FSO) satellite channels are highly dynamic due to atmospheric turbulence, background radiation, weather variability, and finite transmission durations. Most existing models rely on static channel assumptions and asymptotic secret key rate (SKR) estimations, which do not accurately reflect real-time operational conditions. This paper proposes an AI-assisted real-time satellite Continuous Variable QKD (CV-QKD) simulator that integrates live weather data with machine learning- based hybrid noise prediction to model realistic channel behavior. The predicted noise parameters are incorporated into an adaptive QKD framework to dynamically compute both asymptotic and finite-size corrected SKR values. The system further performs day–night comparative analysis and 24-hour temporal simulation to study channel variations over time. All operational parameters, including predicted noise, adaptive SKR, and finite-size adjustments, are logged for reproducibility and performance evaluation. The proposed work implemented in the QKD simulator bridges the gap between theoretical QKD modeling and practical satellite deployment by introducing environmental awareness, AI-driven channel adaptation, and finite-size security considerations within an interactive visualization platform. This framework provides a scalable and realistic tool for analyzing next-generation satellite quantum communication systems.