Autonomous Picosecond-Precision Synchronization in 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 synchronization accuracy better than 10 ps is achievable for channel lengths up to 100 km with realistic optical power levels. The proposed approach improves the scalability and robustness of MDI-QKD architectures and is directly applicable to metropolitan and backbone quantum networks.