  Measurement-device-independent quantum key distribution (MDI-QKD) with
decoy-state method is believed to be securely applied to defeat various hacking
attacks in practical quantum key distribution systems. Recently, the
coherent-state superpositions (CSS) have emerged as an alternative to
single-photon qubits for quantum information processing and metrology. Here, in
this Letter, CSS are exploited as the source in MDI-QKD. We present an
analytical method which gives two tight formulas to estimate the lower bound of
yield and the upper bound of bit error rate. We exploit the standard
statistical analysis and Chernoff bound to perform the parameter estimation.
Chernoff bound can provide good bounds in the long distance MDI-QKD. Our
results show that with CSS, both the security transmission distance and secure
key rate are significantly improved compared with those of the weak coherent
states in the finite-data case.
