LAUSR

Quantum key distribution (QKD) 1 , 2 offers a long-term solution to secure key exchange. Due to photon loss in transmission, it was believed that the repeaterless key rate is bounded by a linear function of the transmittance, O ( η ) (refs. 3 , 4 ), limiting the maximal secure transmission distance 5 , 6 . Recently, a novel type of QKD scheme has been shown to beat the linear bound and achieve a key rate performance of $$O(\sqrt{\eta })$$ O ( η ) (refs. 7 – 9 ). Here, by employing the laser injection technique and the phase post-compensation method, we match the modes of two independent lasers and overcome the phase fluctuation. As a result, the key rate surpasses the linear bound via 302 km and 402 km commercial-fibre channels, over four orders of magnitude higher than existing results 5 . Furthermore, our system yields a secret key rate of 0.118 bps with a 502 km ultralow-loss fibre. This new type of QKD pushes forward long-distance quantum communication for the future quantum internet. Phase-matching quantum key distribution is implemented with a 502 km ultralow-loss optical fibre. The fluctuations of the laser initial phases and frequencies are suppressed by the laser injection technique and the phase post-compensation method.