Quantum key distribution with correlated sources

Implementation security is a critical problem in quantum key distribution (QKD). With the advent of measurement-device-independent QKD, all security loopholes of the measurement unit have been closed. Securing the source, however, remains an elusive issue. Despite the tremendous progress made by developing security proofs that accommodate most typical source imperfections, such proofs usually disregard the effect of pulse correlations. That is, they disregard the fact that the state of an emitted signal can depend on the signals selected previously. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrary pulse correlations. Our method is compatible with those security proofs that accommodate all the other source imperfections, thus paving the way towards achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new security proof, which we call the reference technique, that provides high performance in the presence of source imperfections.