The transmittance fluctuation resulting from free space optics will impart the continuous-variable quantum key distribution (CV-QKD). In this paper, we study the CV-QKD over free space by taking practical transmittance fluctuation into account. The transmittance is modeled following the Gaussian distribution, which reflects the most realistic fluctuation since all sources of perturbation are required to be incorporated together in practice. The comprehensive comparison between the practical model and existing models in secret key rate is drawn. The numerical results reveal that the existing model of uniform distribution underestimates the impact of air link for both slow and fast fading scenarios, and the practical secret key rate will suffer severer degradation. Further, as the variance of the Gaussian model decreases, the secret key rate degrades as well. Also, a comparison between heterodyne and homodyne detection schemes is made, and we found that the heterodyne detection outperforms the homodyne detection in the secret key rate for both the slow and fast fading air quantum channels.
The transmittance fluctuation resulting from free space optics will impart the continuous-variable quantum key distribution (CV-QKD). In this paper, we study the CV-QKD over free space by taking practical transmittance fluctuation into account. The transmittance is modeled following the Gaussian distribution, which reflects the most realistic fluctuation since all sources of perturbation are required to be incorporated together in practice. The comprehensive comparison between the practical model and existing models in secret key rate is drawn. The numerical results reveal that the existing model of uniform distribution underestimates the impact of air link for both slow and fast fading scenarios, and the practical secret key rate will suffer severer degradation. Further, as the variance of the Gaussian model decreases, the secret key rate degrades as well. Also, a comparison between heterodyne and homodyne detection schemes is made, and we found that the heterodyne detection outperforms the homodyne detection in the secret key rate for both the slow and fast fading air quantum channels.
Continuous-variable quantum key distribution (CV-QKD) over air quantum channel enables to provide unconditional information security, which is the one of most promising techniques for information wireless transfer. Since the air channel is of fluctuation in nature due to the presence of air turbulence, the random variations have to be taken into account when the security of CV-QKD is analyzed. We study the secret key rate of CV-QKD over the air quantum channel in this paper. The fluctuation of air channel is characterized by beam wandering and phase distortion under weak air turbulence conditions. The impact of fluctuation on the CV quantum signals is reflected by transmittance perturbation and phase shift. Our numerical results show that the secret key rate may keep relatively high level as the air quantum link increases at the outset. However, when the air link distance further increases beyond certain range, the secret key rate decreases strikingly since the both transmittance perturbation and the phase shift simultaneously deteriorate the performance of CV-QKD. Nevertheless, operating the CV-QKD under weak air turbulence conditions is available.
Abstract This study examines the implementation of continuous-variable quantum key distribution (CV-QKD) using thermal states via fast fading channel. In such channel, communication occurs in free space under adverse conditions such as atmospheric turbulence, causing the channel transmittance to vary according to a specific mathematical probability. In worst-case scenarios, an eavesdropper could fully control the channel, leaving communicators to make pessimistic assumptions about channel conditions. The security of this system is analyzed and evaluated using homodyne and heterodyne detection methods under reverse reconciliation. The results indicate that even with full eavesdropper control, employing noise sources in CV-QKD ensures high key rates and protocol security. Furthermore, it has been demonstrated that the introduction of preparation noise in heterodyne detection is more effective than homodyne detection under fast fading channel conditions.
Continuous-variable quantum key distribution (CV-QKD), which uses quadratures of the electromagnetic field, enables practical quantum communication using standard telecommunication technologies. Unidimensional CV-QKD (UD-CVQKD) simplifies the implementation by restricting modulation to a single quadrature. In this work, we experimentally demonstrate a free-space Gaussian-modulated UD-CVQKD system operating under a high detector electronic-noise regime (1.4 shot-noise units). The system employs polarized coherent states with signal and local oscillator co-propagating in the same spatial mode in orthogonal polarizations, ensuring stable interference. System security is analyzed under both untrusted (UTD) and trusted (TD) detector noise models. While no positive secret key rate is obtained under the UTD model, the TD model enables secure key generation over a finite range of modulation variances, highlighting the critical role of detector trust in high-noise conditions. A maximum secret key rate of 270 kbps is achieved at an optimal modulation variance of 11.57. Furthermore, secure operation requires high-transmittance (low-loss) channels under such noise conditions. This study demonstrates the practical feasibility of free-space UD-CVQKD in realistic high electronic-noise detection constraints and highlights detector electronic noise as a key limiting factor in practical systems.
Compared to fiber continuous-variable quantum key distribution (CVQKD), atmospheric link offers the possibility of a broader geographical coverage and more flexible transmission. However, there are many negative features of the atmospheric channel that will reduce the achievable secret key rate, such as beam extinction and a variety of turbulence effects. Here we show how these factors affect performance of CVQKD, by considering our newly derived key rate formulas for fading channels, which involves detection imperfections, thus form a transmission model for CVQKD. This model can help evaluate the feasibility of experiment scheme in practical applications. We found that performance deterioration of horizontal link within the boundary layer is primarily caused by transmittance fluctuations (including beam wandering, broadening, deformation, and scintillation), while transmittance change due to pulse broadening under weak turbulence is negligible. Besides, we also found that communication interruptions can also cause a perceptible key rate reduction when the transmission distance is longer, while phase excess noise due to arrival time fluctuations requires new compensation techniques to reduce it to a negligible level. Furthermore, it is found that performing homodyne detection enables longer transmission distances, whereas heterodyne allows higher achievable key rate over short distances.
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 (CV-QKD) offers practical advantages for secure communication, but laser linewidth-induced phase noise remains a critical performance limitation. This work presents a comprehensive simulation-based analysis quantifying the impact of laser linewidth on secret key rate (SKR) in Gaussian-modulated coherent-state CV-QKD systems. We develop a detailed noise model incorporating detector electronics, Raman scattering, phase recovery, ADC quantization, and laser relative intensity noise. Through systematic parameter sweeps spanning linewidths from 10 Hz to 250 kHz, modulation variances from 1 to 20 SNU, and fiber distances up to 100 km, we identify three distinct operational regimes and optimization strategies for both transmitted local oscillator (TLO) and local–local oscillator (LLO) configurations under homodyne and heterodyne detection. Results show that metropolitan-scale links (50 km) require linewidths below 5 kHz to maintain secure operation, with performance decreasing beyond 25 kHz. We demonstrate that modulation variance must be jointly optimized with laser quality, with optimal values decreasing from 3–4 SNU at narrow linewidths to 2–2.5 SNU at moderate linewidths. The analysis reveals asymmetric sensitivity in LLO systems where local oscillator linewidth degrades performance more strongly than signal laser linewidth. These quantitative findings provide practical design guidelines for achieving secure CV-QKD operation over metropolitan distances with realistic hardware constraints, supporting deployment of defense-grade quantum communication networks.