Implementation of quantum key distribution surpassing the linear rate-transmittance bound

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(eta) (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(root eta) (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 ultralowloss fibre. This new type of QKD pushes forward long-distance quantum communication for the future quantum internet.