The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate secure key rate, while it still considers that only single-photon pulses can generate secure keys in any case. However, multiphoton pulses can also generate secure keys if we can confirm that there is no attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state protocols, extract a Cauchy distribution statistic, and further provide a detection method and the Type I error probability. If the result is judged to be an attack, we can use the existing decoy-state method and the GLLP formula to estimate secure key rate. Otherwise, all pulses received including both single-photon pulses and multiphoton pulses, can be used to generate the keys and we give the secure key rate in this case. Finally, the associated experiments we performed (i.e., the significance level is $5%$) show the correctness of our method.
Download