Measurement-device-independent quantum key distribution with insecure sources

Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detection side channels but still makes additional assumptions on sources that can be compromised through uncharacterized side channels in practice. Here, we combine a recently proposed reference technique to prove the security of MDI-QKD against possible source imperfections and/or side channels. This requires some reference states and an upper bound on the parameter that describes the quality of the sources. With this formalism we investigate the asymptotic performance of single-photon sources, and the results show that the side channels have a great impact on the key rates.