  Multipartite entanglement enables secure and anonymous key exchange between
multiple parties in a network. In particular Greenberger-Horne-Zeilinger (GHZ)
states have been introduced as resource states for anonymous key exchange
protocols, in which an anonymous subset of parties within a larger network
establishes a secret key. However, the use of other types of multipartite
entanglement for such protocols remains relatively unexplored. Here we
demonstrate that linear cluster states can serve as a versatile and potentially
scalable resource in such applications. We implemented an anonymous key
exchange protocol with four photons in a linear cluster state and established a
shared key between three parties in our network. We show how to optimize the
protocol parameters to account for noise and to maximize the finite key rate
under realistic conditions. As cluster states have been established as a
flexible resource in quantum computation, we expect that our demonstration
provides a first step towards their hybrid use for networked computing and
communication.
