Measurement-device-independent quantum cryptographic conferencing with an untrusted source

Measurement-device-independent quantum cryptographic conferencing (MDI-QCC) protocol puts MDI quantum key distribution (MDI-QKD) forwards to multi-party applications, and suggests a significant framework for practical multi-party quantum communication. In order to mitigate the experimental complexity of MDI-QCC and remove the key assumption (the sources are trusted) in MDI-QCC, we extend the framework of MDI-QKD with an untrusted source to MDI-QCC and give the rigorous security analysis of MDI-QCC with an untrusted source. What is more, in the security analysis we clearly provide a rigorous analytical method for parameter's estimation, which with simple modifications can be applied to not only MDI-QKD with an untrusted source but also arbitrary multi-party communication protocol with an untrusted source. The simulation results show that at reasonable distances the asymptotic key rates for the two cases (with trusted and untrusted sources) almost overlap, which indicates the feasibility of our protocol.