Repeaterless quantum key distribution with efficient finite-key analysis overcoming the rate-distance limit

Quantum key distribution (QKD) over a point-to-point link enables us to benefit from a genuine quantum effect even with conventional optics tools such as lasers and photon detectors, but its capacity is limited to a linear scaling of the repeaterless bound. Recently, twin-field (TF) QKD was conjectured to beat the limit by using an untrusted central station conducting a single-photon interference detection. So far, the effort to prove the conjecture was confined to the infinite key limit which neglected the time and cost for monitoring an adversary's act. Here we propose a variant of TF-type QKD protocol equipped with a simple methodology of monitoring to reduce its cost and provide an information-theoretic security proof applicable to finite communication time. We simulate the key rate to show that the protocol beats the linear bound in a reasonable running time of sending 10¹² pulses, which positively solves the conjecture.