  Anonymous quantum conference key agreement (AQCKA) allows a group of users
within a network to establish a shared cryptographic key without revealing
their participation. Although this can be achieved using bi-partite primitives
alone, it is costly in the number of network rounds required. By allowing the
use of multi-partite entanglement, there is a substantial efficiency
improvement. We experimentally implement the AQCKA task in a six-user quantum
network using Greenberger-Horne-Zeilinger (GHZ)-state entanglement and obtain a
significant resource cost reduction in line with theory when compared to a
bi-partite-only approach. We also demonstrate that the protocol retains an
advantage in a four-user scenario with finite key effects taken into account.
