Finite-key analysis for measurement-device-independent quantum key distribution

The length of signal pulses is finite in practical quantum key distribution. The finite-key analysis of an unconditional quantum key distribution is a burning problem, and the efficient quantum key distribution protocol suitable for practical implementation, measurement-device-independent quantum key distribution (MDI QKD), was proposed very recently. We give the finite-key analysis of MDIQKD, which removes all detector side channels and generates many orders of key rate higher than that of full-device-independent quantum key distribution. The secure bound of the ultimate key rate is obtained under the statistical fluctuations of relative frequency, which can be applied directly to practical threshold detectors with low detection efficiency and highly lossy channels. The bound is evaluated for reasonable values of the observed parameters. The simulation shows that the secure distance is around 10 km when the number of sifted data is 10(10). Moreover the secure distance would be much longer in practice because of some simplified treatments used in our paper.