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) makes the quantum signals more distinguishable thus provides additional information about the quantum signal to an eavesdropper. The explicit eavesdropping strategies aimed at the passive side channel known to date were limited to the separate measurement of the passive side channel in addition to the operational degree of freedom. Here we show how to account for the joint eavesdropping on both operational degree of freedom and the passive side channel of the generic form. In particular, we use the optimal phase-covariant cloning of the signal photon state, which is the most effective attack on the BB84 protocol without side channels, followed by a joint collective measurement of the side channel and the operational degree of freedom. To estimate QKD security under this attack, we develop an effective error method and show its applicability to the BB84 decoy-state protocol.