Measurement-device-independent quantum key distribution (MDI-QKD), which introduces the untrusted third party measurement nodes, is fundamentally immune to all detector side-channel attacks and is a key technology for building wide-area quantum secure communication networks. However, the existing systems typically rely on additional dedicated optical fiber links for clock synchronization between the transmitter and receiver. This not only increases system complexity and deployment costs but also introduces pulse timing misalignment due to mismatched lengths between the synchronization and signal links, resulting in a higher bit error rate. This paper proposes and experimentally demonstrates a common-path clock self-synchronization method based on the second-order correlation properties of the quantum signal itself. This method uses the second-order correlation function of the pseudo-random displacement optical pulse sequences sent by both communication parties as the clock synchronization criterion. It directly extracts the channel delay information from the quantum signal in real time and performs closed-loop feedback compensation via a tunable optical fiber delay line, thereby eliminating, in principle, the inherent drift risks associated with non-common-path transmission.
In this paper, first, we establish a complete theoretical model based on the second-order correlation characteristics of the optical pulse sequences. Starting with the sequences of pseudo-random displacement optical pulses emitted by the two communicating parties, this model analyzes the evolution of their cross-correlation functions under the optical fiber channel dynamic drift. It establishes a quantitative mapping between the characteristic peaks of the correlation function and the path delay difference, thereby laying the theoretical foundation for extracting synchronization information in real time from the quantum signals themselves and providing a basis for closed-loop compensation. Second, we develope a clock self-synchronization experimental system with closed-loop feedback control capabilities. Both the transmitter and receiver use the GPS reference clocks and employ the arbitrary waveform generators to modulate optical pulses with identical pseudo-random time displacement sequences. By measuring the second-order correlation function between the two pulse sequences, the receiver can accurately extract real-time relative delay information of the optical fiber link. This information is then used to dynamically compensate for the delay through feedback control of a tunable fiber delay line, thereby achieving adaptive synchronization of the transmitter clock. Finally, we validate the self-synchronization theory through the experiments. Under the different delay conditions, we measure the second-order correlation function of the optical pulse sequences encoded with pseudo-random displacement. The experiment results confirm the quantitative mapping relationship between the characteristic peak positions of the second-order correlation function and the path delay differences. Over a 100 km optical fiber link, we achieve a long-term synchronization accuracy better than 77.7 ps (RMS) and demonstrate that the system can effectively track and compensate for the linear delay drifts of up to 7.8 ps/s.
In conclusion, this work abandons traditional independent synchronization links, thereby avoiding the inherent drift problems caused by non-common-path transmission. It develops a high-precision, low-complexity clock self-synchronization technology for MDI-QKD systems, and provides offers a viable technical pathway for promoting their practical deployment.