  Sharing multi-partite quantum entanglement between parties allows for diverse
secure communication tasks to be performed. Among them, conference key
agreement (CKA), an extension of key distribution to multiple parties, has
received much attention recently. Interestingly, CKA can also be performed in a
way that protects the identities of the participating parties, therefore
providing anonymity. In this work, we propose an anonymous CKA protocol for
three parties that is implemented in a highly practical network setting.
Specifically, a line of quantum repeater nodes is used to build a linear
cluster state among all nodes, which is then used to anonymously establish a
secret key between any three of them. The nodes need only share maximally
entangled pairs with their neighbours, therefore avoiding the necessity of a
central server sharing entangled states. This repeater setup makes our protocol
an excellent candidate for implementation in future quantum networks. We
explicitly prove that our protocol protects the identities of the participants
from one another and perform an analysis of the key rate in the finite regime,
contributing to the quest of identifying feasible quantum communication tasks
for network architectures beyond point-to-point.
