Measurement-device-independent quantum key distribution (MDI-QKD) has beendemonstrated in both laboratories and field-tests using attenuated laserscombined with the decoy-state technique. Although researchers have studiedvarious decoy-state MDI-QKD protocols with two or three decoy states, a clearcomparison between these protocols is still missing. This invokes the questionof how many types of decoy states are needed for practical MDI-QKD. Moreover,the system parameters to implement decoy-state MDI-QKD are only partiallyoptimized in all previous works, which casts doubt on the actual performance offormer demonstrations. Here, we present analytical and numerical decoy-statemethods with one, two and three decoy states. We provide a clear comparisonamong these methods and find that two decoy states already enable a nearoptimal estimation and more decoy states cannot improve the key rate much ineither asymptotic or finite-data settings. Furthermore, we perform a fulloptimization of system parameters and show that full optimization cansignificantly improve the key rate in the finite-data setting. By simulating areal experiment, we find that full optimization can increase the key rate bymore than one order of magnitude compared to non-optimization. A local searchmethod to optimize efficiently the system parameters is proposed. This methodcan be four orders of magnitude faster than a trivial exhaustive search toachieve a similar optimal key rate. We expect that this local search methodcould be valuable for general fields in physics.
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