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 \(O(\sqrt{\eta })\) (refs. ^7,8,9). 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 results⁵. 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.

量子密钥分配（QKD）^1,2提供了一种长期解决方案，可确保密钥交换的安全。由于光子在传输中的损失，人们认为无中继器的密钥速率受透射率的线性函数O（η）（参考^3,4）的限制，从而限制了最大安全传输距离^5,6。最近，一种新型的QKD方案已被证明可以克服线性边界并达到\（O（\ sqrt {\ eta}）\）的关键速率性能（参考文献^7,8,9）。在这里，通过采用激光注入技术和相位后补偿方法，我们匹配了两个独立激光器的模式，并克服了相位波动。结果，关键速率通过302 km和402 km商业光纤通道超过了线性范围，比现有结果高出四个数量级⁵。此外，我们的系统使用502公里超低损耗光纤可产生0.118 bps的秘密密钥速率。这种新型的QKD推动了未来量子互联网的长距离量子通信。