Experimental quantum conference key agreement

Future quantum networks will enable long-distance quantum key distribution (QKD) by providing on-demand entanglement to arbitrary combinations of users.Paradigmatic QKD protocols establish secure keys between pairs of users, however when more than two parties want to communicate, recently introduced quantum conference quantum key agreement (CKA) protocols can drastically outperform 2-party primitives in terms of resource cost. Here we implement a four-user quantum CKA protocol using polarisation-encoded Greenberger-Horne-Zeilinger (GHZ) entangled states generated by high-brightness, telecom photon-pair sources. We distribute these states over fibre connections of up to 50 km length and implement custom multi-party error correction and privacy amplification on the resulting raw keys. From a finite-key analysis, we establish an information-theoretic secure key of up to $1.15\times10^6$ bits, which is used to encrypt and securely share an image between the four users. Surpassing the previous maximum distance for GHZ state transmission by more than an order of magnitude, these results demonstrate the viability of network protocols relying on multi-partite entanglement. Future applications beyond quantum CKA include entanglement-assisted remote clock-synchronization, quantum secret sharing, and GHZ-based repeater protocols.