Device-independent quantum key distribution with random postselection

Device-independent quantum key distribution (QKD) can permit the superior security even with unknown devices. In practice, however, the realization of device-independent QKD is technically challenging because of its low noise tolerance. In photonic setup, due to the limited detection efficiency, a large amount of the data generates from no-detection events which contain little correlations but contribute high errors. Here we propose the device-independent QKD protocol with random post selection, where the secret keys are extracted only from the post-selected subset of outcomes. This could not open the detection loophole as long as the entropy of the post-selected subset is evaluated from the information of the entire set of data, including both detection and no-detection events. This post selection has the advantage to significantly reduce the error events, thus relaxing the threshold of required detection efficiency. In the model of collective attacks, our protocol can tolerate detector efficiency as low as 68.5%, which goes beyond standard security proofs. The results make a concrete step for the implementation of device-independent QKD in practice.