Joint Eavesdropping on the BB84 Decoy State Protocol with an Arbitrary Passive Light-source Side Channel

Passive light-source side channel in quantum key distribution (QKD) provides additional information to an eavesdropper via various non-operational degrees of freedom of the optical signal. The currently known explicit eavesdropping strategies aimed at additional information gain from the passive light-source side channel were limited to the attack on the side channel and the operational degree of freedom separately. As a result, their efficiency is far from being optimal. Here we provide the joint eavesdropping strategy on both operational degree of freedom and the passive light-source side channel of the generic form, and develop a method to calculate the corresponding secret key rate. In particular, we use the optimal phase-covariant cloning of the signal photon state followed by a joint collective measurement of the side channel and the operational degree of freedom. To estimate security under the explicit attack strategy, we develop an ‘‘effective error’’ method and demonstrate it on the BB84 protocol with decoy states. Our work extends the practical analysis of QKD protocols with the light-source side channels and can be used as a tool for the analysis of realistic eavesdropping methods.