Excess leakage of information in quantum key distribution with passive side channels

Passive side channels of the photon source make quantum key distribution (QKD) protocols insecure. To restore security, we need to incorporate the leakage through the side channel into the secret key estimate, but there is no definitive way to do that. In this work, we compare several practical methods of secret key rate estimating in QKD protocols with photon distinguishability side channel. We calculate upper bounds on secret key generation rates, using two reinterpretations of eavesdropper excess information - the effective error method and the a-priori loss method. We demonstrate that the effective error method provides tighter upper bound on the secret key rate than a- priori loss. Our results refine the toolbox of estimating security of QKD protocols with passive source side channels.