  The ability to distribute entanglement over complex quantum networks is an
important step towards a quantum internet. Recently, there has been significant
theoretical effort, mainly focusing on the distribution of bipartite
entanglement via a simple quantum network composed only of bipartite quantum
channels. There are, however, a number of quantum information processing
protocols based on multipartite rather than bipartite entanglement. Whereas
multipartite entanglement can be distributed by means of a network of bipartite
channels, a more natural way is to use a more general network, that is, a
quantum broadcast network including quantum broadcast channels. In this work,
we present a general frame- work for deriving upper bounds on the rates at
which GHZ states or multipartite private states can be distributed among a
number of different parties over an arbitrary quantum broadcast network. Our
upper bounds are written in terms of the multipartite squashed entanglement,
corresponding to a generalisation of recently derived bounds [K. Azuma et al.,
Nat. Commun. 7, 13523 (2016)]. We also discuss how lower bounds can be obtained
by combining a generalisation of an aggregated quantum repeater protocol with
graph theoretic concepts.
