Fundamental limitation on quantum broadcast networks

TL;DR

This paper establishes fundamental upper bounds on distributing multipartite entanglement over quantum broadcast networks, extending previous bipartite-focused results and providing a framework for future quantum internet development.

Contribution

It introduces a general framework for bounding the rates of multipartite entanglement distribution over quantum broadcast networks using multipartite squashed entanglement.

Findings

Upper bounds on GHZ and private state distribution rates derived

Framework generalizes previous bipartite bounds to multipartite networks

Discussion on lower bounds via quantum repeater protocols and graph theory

Abstract

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.