Abstract
Without any assumption on detectors, measurement-device-independent quantum random-number generators (MDI QRNGs) with high generation rates have attracted lots of attention lately. However, the influence of statistical fluctuations on randomness extraction rate has not been taken into full consideration, which is crucial in the practical applications of MDI QRNGs. We propose a solution for MDI QRNGs, study the influence of statistical fluctuations, and apply an optimizing method to solve the lower bound of randomness extraction rate. Then the rate is simulated under reasonable values of some observed parameters, and it displays that the QRNG generates $6\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{4pt}{0ex}}\text{bit}/\text{s}$, if the transmission loss is 10 dB and the number of pulses sent from the source is $N={10}^{12}$. Compared with the rates of other MDI QRNGs, our simulation outputs are with genuine randomness, since the statistical fluctuations of all parameters are considered.
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