  Measurement-device-independent quantum key distribution (MDI-QKD) with weak
coherent sources has been widely and meticulously analyzed. However, the
analysis for MDI-QKD with spontaneous parametric-down-conversion sources
(SPDCS) is incomplete. In this paper, by accounting for practical parameters of
SPDCS with thermal distribution, we presents an investigation on the
performances of MDI-QKD under the active three-intensity decoy protocol and the
passive one-intensity decoy protocol respectively. Phase randomization,
inherently prerequisite for decoy protocol, is taken into consideration for
evaluating the overall quantum bit gain and quantum bit error rate. The
numerical simulations show that MDI-QKD using SPDCS with practical decoy
protocols can be demonstrated comparable to the asymptotical case with infinite
decoy states and has apparent superiority both in transmission distance and key
generation rate compared to the MDI-QKD using weak coherent sources. Our
results also indicate that MDI-QKD using thermal distributed SPDCS with active
three-intensity decoy protocol performs better than the one with passive
one-intensity decoy protocol.
