Measurement-device-independent quantum key distribution with insecure sources

Measurement-device-independent quantum key distribution (MDI-QKD) can eliminate all detector side-channel loopholes and has shown excellent performance in long-distance secret keys sharing. Conventional security proofs, however, require additional assumptions on sources and that can be compromised through uncharacterized side channels in practice. Here, we present a general formalism based on reference technique to prove the security of MDI-QKD against any possible sources imperfection and/or side channels. With this formalism, we investigate the asymptotic performance of single-photon sources without any extra assumptions on the state preparations. Our results highlight the importance of transmitters' security.