Detecting the possibility of a type of photon number splitting attack in decoy-state quantum key distribution

The existing decoy-state quantum key distribution(QKD)beating photon-number-splitting(PNS)attack provides a more accurate method to estimate the 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 detect the possibility of PNS attack in the channel.The ultimate goal of this line of research is to confirm the absence of all types of PNS attacks.In particular,the PNS attack mentioned and detected in this paper is only the weaker version of PNS attack which significantly changes the observed values of the legitimate users.In this paper,under the null hypothesis of no weaker version of 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 the secure key rate.Otherwise,the pulses with the same basis 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.