Fundamental limitation on quantum broadcast networks

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.