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 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(eta(N)) to O(eta(N-1)) compared with the measurement device-independent QCC protocols. Meanwhile, it can be easily scaled up to multiple parties due to its simple setup.