On the Impact of Tracking Inaccuracy in Space-Based Quantum Key Distribution: A Stochastic Geometric Approach

This paper investigates the performance of satellite-based quantum key distribution (QKD) under realistic channel conditions, emphasizing the adverse effects of photon loss introduced by pointing errors and the presence of background photons. By leveraging a stochastic framework, we model the probability distribution of the number of photons detected at the receiver, considering Gaussian beam propagation, finite receiver aperture, and Poisson-distributed background noise. We then evaluate essential QKD performance metrics - such as the quantum key rate, quantum bit error rate (QBER), and outage probability - across a wide range of beam waist sizes and tracking accuracies. Numerical simulations demonstrate how subtle increases in the pointing error variance can drastically reduce the secure key generation rate, particularly for tightly focused beams. These findings highlight the importance of precise pointing systems and careful selection of optical parameters to ensure an acceptable QBER and a sufficiently high secret key rate in inter-satellite QKD links.