Autonomous Picosecond-Precision Synchronization in Measurement-Device-Independent Quantum Key Distribution

Abstract: 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.