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 the photonic setup, due to the limited detection efficiency, a large amount of the data generates from no-detection events which contain few correlations but contribute high errors. Here, we propose the device-independent QKD protocol with random postselection, where the secret keys are extracted only from the postselected subset of outcomes. This could not open the detection loophole as long as the entropy of the postselected subset is evaluated from the information of the entire set of data, including both detection and no-detection events. This postselection 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.

Figure 1

Photonic realization of the device-independent QKD. A quantum state created by a source that is potentially controlled by Eve is shared between Alice and Bob. Alice and Bob perform measurements using a polarizing beam splitter (PBS) and two detectors. A set of wave plates $[(\lambda /4),(\lambda /2)]$ allow them to choose the measurement setting. Each party effectively produces one of two possible outcomes 0 and 1.

Figure 2

Asymptotic secret key rate as a function of detection efficiency. In the scenario of random postselection, the protocol can tolerate efficiency as low as $\eta \approx 68.5\%$ (red-solid curve). The black dot-dashed curve comes from Ref. [17], which shows positive key rate with threshold efficiency $\eta \approx 92.4\%$. The blue-dashed curve is obtained when using the protocol of noisy pre-processing [33, 35], and it shows a threshold efficiency of $\eta \approx 82.6\%$.