  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.
