Proving security of BB84 under source correlations

Device imperfections and memory effects can result in undesired correlations among the states generated by a realistic quantum source. These correlations are called source correlations. Proving the security of quantum key distribution (QKD) protocols in the presence of these correlations has been a persistent challenge. We present a simple and general method to reduce the security proof of the BB84 protocol with source correlations to one with an almost perfect source, for which security can be proven using previously known techniques. For this purpose, we introduce a simple source test, which randomly tests the output of the QKD source and provides a bound on the source correlations. We then use the recently proven entropic triangle inequality for the smooth min-entropy to carry out the reduction to the protocol with the almost perfect source.