Composable Finite-Size Security of High-Dimensional Quantum Key Distribution Protocols

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.