Frequency-matching quantum key distribution

Quantum key distribution (QKD) enables information-theoretically secure communication against eavesdropping. However, phase instability remains a challenge across many QKD applications, particularly in schemes such as twin-field QKD and measurement-device-independent QKD. The most dominant source of phase fluctuation arises from the frequency offset between independent lasers. Here we propose a method to address this issue by employing a classical photodiode to compensate for the laser frequency difference. As an application of this method, we implement this technique in a mode-pairing QKD system, achieving an error rate approaching the theoretical limit and surpassing the linear key-rate bound over a fiber distance of 296.8 km. This approach provides a practical solution for frequency matching between independent lasers and can be extended to other fields requiring precise phase stabilization.