Phase-Matching Quantum Cryptographic Conferencing

Quantum cryptographic conferencing (QCC) holds promise for distributing information-theoretic secure keys among multiple users over a long distance. Limited by the fragility of Greenberger-Horne-Zeilinger (GHZ) states, QCC networks based on directly distributing GHZ states over a long distance still face a big challenge. Another two potential approaches are measurement device-independent QCC and conference-key agreement with single-photon interference, which were proposed on the basis of the postselection of GHZ states and the postselection of the W state, respectively. However, implementations of the former protocol are still heavily constrained by the transmission rate $\ensuremath{\eta}$ of optical channels and the complexity of the setups for postselecting GHZ states. Meanwhile, the latter protocol cannot be cast as a measurement device-independent prepare-and-measure scheme. Combining the idea of postselecting GHZ states and recently proposed twin-field quantum-key-distribution protocols, we report a QCC protocol based on weak coherent-state interferences named ``phase-matching quantum cryptographic conferencing,'' which is immune to all detector side-channel attacks. The proposed protocol can improve the key-generation rate from $O({\ensuremath{\eta}}^{N})$ to $O({\ensuremath{\eta}}^{N\ensuremath{-}1})$ compared with the measurement device-independent QCC protocols. Meanwhile, it can be easily scaled up to multiple parties due to its simple setup.