Decoy-state measurement-device-independent quantum key distribution based on the Clauser-Horne-Shimony-Holt inequality

The measurement-device-independent quantum key distribution (MDI-QKD) protocol is proposed to remove the detector side channel attacks, while its security relies on the assumption that the encoding systems are perfectly characterized. In contrast, the MDI-QKD protocol based on the Clauser-Horne-Shimony-Holt inequality (CHSH-MDI-QKD) weakens this assumption, which only requires the quantum state to be prepared in the two-dimensional Hilbert space and the devices are independent. In experimental realizations, the weak coherent state, which is always used in QKD systems due to the lack of an ideal single-photon source, may be prepared in the high-dimensional space. In this paper, we investigate the decoy-state CHSH-MDI-QKD protocol with s (3≤s≤5) intensities, including one signal state and s -1 decoy states, and we also consider the finite-size effect on the decoy-state CHSH-MDI-QKD protocol with five intensities. Simulation results show that this scheme is very practical.