  Measurement-device-independent quantum key distribution (MDI-QKD) has been
demonstrated in both laboratories and field-tests using attenuated lasers
combined with the decoy-state technique. Although researchers have studied
various decoy-state MDI-QKD protocols with two or three decoy states, a clear
comparison between these protocols is still missing. This invokes the question
of how many types of decoy states are needed for practical MDI-QKD. Moreover,
the system parameters to implement decoy-state MDI-QKD are only partially
optimized in all previous works, which casts doubt on the actual performance of
former demonstrations. Here, we present analytical and numerical decoy-state
methods with one, two and three decoy states. We provide a clear comparison
among these methods and find that two decoy states already enable a near
optimal estimation and more decoy states cannot improve the key rate much in
either asymptotic or finite-data settings. Furthermore, we perform a full
optimization of system parameters and show that full optimization can
significantly improve the key rate in the finite-data setting. By simulating a
real experiment, we find that full optimization can increase the key rate by
more than one order of magnitude compared to non-optimization. A local search
method to optimize efficiently the system parameters is proposed. This method
can be four orders of magnitude faster than a trivial exhaustive search to
achieve a similar optimal key rate. We expect that this local search method
could be valuable for general fields in physics.
