Autonomous Picosecond-Resolution Synchronization Algorithm for Measurement-Device-Independent Quantum Key Distribution

Measurement-device-independent quantum key distribution (MDI-QKD) eliminates detector side-channel attacks by relocating all measurements to an untrusted intermediate node. However, its practical implementation critically relies on picosecond-level temporal synchronization between spatially separated users. In this work, we present a physically motivated autonomous synchronization algorithm for fiber-based MDI-QKD networks that does not require auxiliary optical channels or shared clock references. The method exploits round-trip optical pulse propagation and statistical signal detection in the presence of Gaussian noise. We derive analytical expressions for false-alarm probabilities, quantify detection reliability, and demonstrate through numerical modeling that a scanning resolution of 10 ps is achievable for channel lengths of up to 100 km with realistic optical power levels. The actual timing accuracy is limited by detector, source, and electronic jitter and is not quantified in this work. The proposed approach improves the scalability and robustness of MDI-QKD architectures and is directly applicable to metropolitan and backbone quantum networks.