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 $s(3\le s\le 5)$ 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.

Figure 1

Results of the decoy-state CHSH-MDI-QKD protocol and the decoy-state MDI-QKD protocol with different intensities in the asymptotic case. Note that D denotes the decoy states, and S denotes the signal state.

Figure 2

Results of the decoy-state CHSH-MDI-QKD protocol with five intensities with statistical fluctuation.