Practical implementations of quantum key distribution (QKD) extending beyond urban areas commonly use satellite links; however, the transmission of quantum states through the Earth’s atmosphere is highly susceptible to noise, restricting its application primarily to nighttime. High-dimensional (HD) QKD offers a promising solution to this limitation by employing high-dimensionally entangled quantum states. Although experimental platforms for HD QKD exist, previous security analyses have been limited to the asymptotic regime and have either relied on impractical measurements or employed computationally demanding convex optimization tasks, restricting the security analysis to low dimensions. In this work, we bridge this gap by presenting a composable finite-size security proof against both collective and coherent attacks for a general HD QKD protocol that uses only experimentally accessible measurements. In addition to the conventional yet impractical “one-shot” key rates, we provide a practical variable-length security argument that yields significantly higher expected key rates. This approach is particularly crucial under rapidly changing and turbulent atmospheric conditions, as encountered in free-space and satellite-based QKD platforms.
Practical implementations of quantum key distribution (QKD) extending beyond urban areas commonly use satellite links; however, the transmission of quantum states through the Earth’s atmosphere is highly susceptible to noise, restricting its application primarily to nighttime. High-dimensional (HD) QKD offers a promising solution to this limitation by employing high-dimensionally entangled quantum states. Although experimental platforms for HD QKD exist, previous security analyses have been limited to the asymptotic regime and have either relied on impractical measurements or employed computationally demanding convex optimization tasks, restricting the security analysis to low dimensions. In this work, we bridge this gap by presenting a composable finite-size security proof against both collective and coherent attacks for a general HD QKD protocol that uses only experimentally accessible measurements. In addition to the conventional yet impractical “one-shot” key rates, we provide a practical variable-length security argument that yields significantly higher expected key rates. This approach is particularly crucial under rapidly changing and turbulent atmospheric conditions, as encountered in free-space and satellite-based QKD platforms.
High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints; thus, accessible dimensions are far exceeded by progress in HD photonics, bringing forth a need for efficient methods to compute key rates for large encoding dimensions. In response to this problem, we present a flexible analytic framework facilitated by the dual of a semidefinite program and diagonalizing operators inspired by entanglement-witness theory, enabling the efficient computation of key rates in high-dimensional systems. To facilitate the latter, we show how matrix completion techniques can be incorporated to effectively yield improved, computable bounds on the key rate in paradigmatic high-dimensional systems of time- or frequency-bin entangled photons and beyond, revealing the potential for very high-dimensions to surpass low dimensional protocols already with existing technology. In our accompanying work, (F. Kanitschar and M. Huber, Composable finite-size security of high-dimensional quantum key distribution protocols), available on arXiv, we show how our findings can be used to establish finite-size security against coherent attacks for general HD-QKD protocols both in the fixed- and variable-length scenario.
High-dimensional quantum key distribution (HD-QKD) provides notable advantages over qubit-based QKD, including higher key rates and greater noise resilience. Leveraging the orbital angular momentum states of structured photons to encode information has become a prominent method for implementing HD-QKD. However, practical challenges such as state-dependent diffraction, limited receiving aperture, and atmospheric turbulence impose constraints on the attainable performance and encoding dimension of QKD in free-space links. In this work, we address these challenges with focused, structured photons. Numerical simulations indicate that this method markedly enhances transmission efficiency and improves the robustness against turbulence, resulting in higher key rates and extended transmission distances in free-space HD-QKD. Additionally, focused, structured photons allow us to implement higher-dimensional QKD and enable QKD systems to achieve superior performance with smaller receiving apertures in a turbulent free-space link. This makes our approach particularly advantageous for applications of unmanned aerial vehicles and satellite platforms. Our work contributes to exploring the robust QKD schemes employing structured photons and may promote its application in quantum networks.
Discrete-Modulated (DM) Continuous-Variable (CV) Quantum Key Distribution (QKD) is an experimentally attractive approach to quantum cryptography, offering high key rates over metropolitan-scale distances while relying on state-of-the-art telecom infrastructure. However, a fundamental gap has remained between this experimental promise and rigorous security: for more than two decades, DM CV-QKD has lacked a complete composable finite-size security proof against coherent attacks. Existing works either restrict the adversary to collective attacks, impose additional finite-dimensional assumptions, apply only to specific modulation formats, or fail to recover the known asymptotic rates. Here, we resolve this longstanding problem by establishing the first complete composable finite-size security proof for DM CV-QKD protocols against coherent attacks, incorporating imperfect detectors and both fixed- and variable-length protocol variants. Our proof introduces two central results of broader interest: an infinite-dimensional marginal-constrained entropy accumulation theorem (iMEAT) and a rigorous dimension-reduction technique that makes the infinite-dimensional security bounds numerically tractable. The resulting key rates recover the known asymptotic rates and outperform established finite-size bounds based on collective attacks, while yielding positive key rates beyond 70km for experimentally relevant block sizes and parameters. Thus, our work closes a longstanding gap and places an experimentally attractive class of CV-QKD protocols on a rigorous composable security footing and provides a pathway towards their practical deployment.
High-dimensional states (HD) are promising for quantum key distribution (QKD) due to their noise tolerance and efficiency. However, creating, and measuring, HD states is technologically challenging, thus making it important to study HD-QKD protocols where Alice and Bob are restricted in their quantum capabilities. In this paper, we revisit an HD-QKD protocol, introduced in (PRA 97 (4):042347), which does not require Alice and Bob to be capable of sending and measuring in full mutually unbiased bases. The previous proof of security for this protocol has relied on numerical methods. In this work, we provide a new proof of security, enabling the key-rate evaluation beyond previous work. Furthermore, our new proof produces better results for certain channel and dimension scenarios than prior work.
Quantum key distribution (QKD) brings the promise of communication with information-theoretic security but is limited in practice due to its susceptibility to noise, losses, and device imperfections. To address these challenges, we propose a robust high-dimensional (HD) one-sided device-independent QKD (1sDI-QKD) protocol and present a proof-of-principle experimental implementation using photons entangled in the transverse-spatial degree-of-freedom. We develop a systematic security analysis of HD 1sDI-QKD protocols, leveraging quantum steering to certify security, and evaluate achievable secret key rates for different measurement configurations and system dimensions using reverse reconciliation. Our analysis shows that increasing the dimension enhances robustness against both noise and loss. We then demonstrate the key experimental building blocks required for implementing the protocol: (a) a high-quality source of high-dimensional photonic entanglement, and (b) a fully programmable, high-dimensional multi-outcome measurement device operating in up to dimension 11. Using these components, we obtain positive key rates for all investigated dimensions under the fair-sampling assumption, with the highest key rates achieved for dimension d=7. Finally, we discuss the steps required for a practical, loophole-free implementation of 1sDI-QKD in realistic regimes of loss and noise.
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.