Decoy-state method of quantum key distribution with both source errors and statistics fluctuations

The effects of statistical fluctuation and vacuum source fluctuation on the decoy-state method with an unstable decoy source and signal source are studied. The method is improved by a tightened estimation of the vacuum count. Compared with the existing results with an unstable vacuum source and statistical fluctuation, the results presented here have improved the key rate of the 3-intensity protocol for quantum key distribution.