Abstract A systematic analysis of the advantages and challenges associated with the satellite‐based implementation of the high dimensional extended B92 (HD‐Ext‐B92) and high‐dimensional BB84 (HD‐BB84) protocol is analyzed. The method used earlier for obtaining the key rate for the HD‐Ext‐B92 is modified here and subsequently the variations of the key rate, probability distribution of key rate (PDR), and quantum bit error rate (QBER) with respect to dimension and noise parameter of a depolarizing channel is studied using the modified key rate equation. Further, the variations of average key rate (per pulse) with zenith angle and link length in different weather conditions in day and night considering extremely low noise for dimension are investigated using elliptic beam approximation. The effectiveness of the HD‐(extended) protocols used here in creating satellite‐based quantum key distribution links (both up‐link and down‐link) are established by appropriately modeling the atmosphere and analyzing the variation of average key rates with the probability distribution of the transmittance (PDT). The analysis performed here has revealed that in higher dimensions, HD‐BB84 outperforms HD‐Ext‐B92 in terms of both key rate and noise tolerance. However, HD‐BB84 experiences a more pronounced saturation of QBER in high dimensions.
Abstract A systematic analysis of the advantages and challenges associated with the satellite‐based implementation of the high dimensional extended B92 (HD‐Ext‐B92) and high‐dimensional BB84 (HD‐BB84) protocol is analyzed. The method used earlier for obtaining the key rate for the HD‐Ext‐B92 is modified here and subsequently the variations of the key rate, probability distribution of key rate (PDR), and quantum bit error rate (QBER) with respect to dimension and noise parameter of a depolarizing channel is studied using the modified key rate equation. Further, the variations of average key rate (per pulse) with zenith angle and link length in different weather conditions in day and night considering extremely low noise for dimension are investigated using elliptic beam approximation. The effectiveness of the HD‐(extended) protocols used here in creating satellite‐based quantum key distribution links (both up‐link and down‐link) are established by appropriately modeling the atmosphere and analyzing the variation of average key rates with the probability distribution of the transmittance (PDT). The analysis performed here has revealed that in higher dimensions, HD‐BB84 outperforms HD‐Ext‐B92 in terms of both key rate and noise tolerance. However, HD‐BB84 experiences a more pronounced saturation of QBER in high dimensions.
Quantum Key Distribution (QKD) has emerged as a fundamentally secure approach to communication in the era of quantum computing, offering protection against threats posed to classical cryptographic schemes such as RSA and Diffie-Hellman. This thesis presents a comprehensive performance analysis of satellite-based QKD protocols, focusing on both prepare-and-measure and entanglement-based schemes under realistic atmospheric and operational conditions. The study begins by introducing the theoretical foundations of quantum communication, including qubits, entanglement, and quantum entropy, and motivates the need for satellite-based QKD to overcome the distance limitations of fiber-based systems. Subsequently, the thesis evaluates four prominent QKD protocols-BB84, B92, BBM92, and E91-using a circular beam propagation model that incorporates atmospheric effects such as diffraction, turbulence, attenuation, and pointing errors, along with environmental noise contributions for uplink and downlink. Comparative numerical simulations reveal that protocol performance is strongly influenced by channel asymmetries, beam propagation characteristics, and noise, providing guidance on optimal protocol selection for low Earth orbit (LEO) satellite links. The research further investigates high-dimensional (HD) QKD protocols, specifically HD-BB84 and HD-Extended B92, using the elliptic-beam approximation to account for turbulence-induced distortions for both uplink and downlink. Simulations under vary ing system dimensions, weather conditions, and zenith angles demonstrate that HD-BB84 achieves higher key rates, superior noise tolerance, and more favorable probability distributions of the key rate compared to HD-Extended B92, highlighting the advantages of high-dimensional encoding for robust satellite-based QKD.
Satellite-based free-space quantum key distribution (QKD) provides a practical framework for achieving secure global communication beyond the limitations of optical fibers. In this work, the quantum bit error rate (QBER) and secure key rate of four representative protocols-BB84, B92, BBM92, and E91 are investigated over low earth orbit (LEO) links in both uplink and downlink configurations. The optical link is modeled using a Gaussian beam formalism, incorporating the effects of diffraction, pointing errors, atmospheric turbulence, and background noise contributions. The protocols are examined under day and night-time operating conditions, and their dependence on the zenith angle is analyzed. The findings show that downlink links generally exhibit lower QBER and higher secure key rates than uplinks, and among prepare-and-measure schemes, BB84 consistently outperforms B92, while in entanglement-based approaches, BBM92 achieves higher key rates than E91.
Abstract This study investigates the feasibility of the phase‐matching measurement‐device‐independent quantum key distribution (PM‐MDI QKD) protocol proposed by Lin and Lütkenhaus for satellite‐based quantum communication. The protocol's key rate, known to exceed the repeaterless PLOB bound, is evaluated in the asymptotic limit under noisy conditions typical of satellite communications, including loss‐only scenarios. The setup involves two ground‐based parties connected via fiber (loss‐only or noisy) and a space‐based third party linked to one of these two ground‐based parties through free‐space communication. Simulations using the elliptic‐beam approximation model the average key rate (AKR) and its probability distribution (PDR) across varying zenith angles and fiber distances. Down‐link free‐space communication is assessed under day and night conditions, with intensity optimization for each graphical point. Dynamic configurations of satellite and ground stations are also considered. Results indicate that AKR decays more slowly under loss‐only conditions, while PDR analysis shows higher key rates produce more concentrated distributions. These findings demonstrate the potential of PM‐MDI QKD protocols for achieving reliable key rates in satellite‐based quantum communication.
Abstract Quantum Key Distribution (QKD) via CubeSats presents a promising pathway for secure global communication. However, realistic modeling of the satellite-to-ground optical link remains a challenge due to beam divergence, atmospheric turbulence and finite key effects. In this work, we employed an elliptical beam approximation model for the downlink channel to more accurately characterize transmittance variations compared to conventional circular beam models. This refined approach facilitates a precise estimation of finite and asymptotic key rates under realistic weather conditions, for weak coherent pulse (WCP)-based efficient BB84 and standard BB84 protocols using two decoy states in a CubeSat-based downlink scenario. Our results reveal that the efficient BB84 protocol consistently yields higher key rates, particularly under turbulent conditions, making it more suitable for practical deployment. Additionally, we analyze probability distribution of key rate (PDR) across different zenith angles demonstrating the robustness of elliptical beam modeling for CubeSat-based QKD. This study provides an improved framework for designing realistic CubeSat-based QKD systems, bridging theoretical models and experimental feasibility.
The quantum based satellite communication offers a secure way for key distribution which is essential for symmetric keys based transmi ssion. For modeling this type of communication, we created a mathematical model which is based on the behavior of singlephoton sources and detectors and on the losses orig inated from beam spreading and pointing error. Based on this model, we developed a simulator software to study the quantum communication over space-space links, e.g., between two satellites. We analyzed the performance of three quantum key distribution protocols—BB84, B92, S09—on different space-space links. Two of the main parameters during the analysis were the size of the necessary aperture for a successful space-space communication and the length of the communication channel. Our results show that the three mentioned QKD protocols are feasible when using satellite-satellite links.
Abstract The performance of single photon pulsed polarization based BB84 and B92 platforms against individual attacks for free space quantum optical communication links between a ground station and a satellite in the low earth orbit is compared. The comparison is attained by evaluating the quantum bit error rate and secure communication bit rate on secure optical link loss and the sensitivity of different parameters. Precisely, realistic experimental parameters are used and the obtained results are compared with those of other papers. Quantum bit error rates as low as 3.5% have been regularly obtained. Moreover, with repetition rate of 10MHz at the low earth orbit standard orbital altitude of 100 km and at zenith angle of 60 degrees, secure communication bit rates of ~ 280 kHz and ~ 70 kHz were received for the BB84 and B92, respectively. The obtained results show that the BB84 protocol exhibits better performance than B92 in the distribution of the secure communication key over long distance. Overall, these results reveal that it is possible to obtain secure key exchange in the low earth orbit, an idea which can be extended to other long distance laser links such as geostationary orbit.