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The study of entanglement in multipartite quantum states plays a major rolein quantum information theory and genuine multipartite entanglement signals oneof its strongest forms for applications. However, its characterization forgeneral (mixed) states is a highly nontrivial problem. We introduce aparticularly simple subclass of multipartite states, which we termpair-entangled network (PEN) states, as those that can be created bydistributing exclusively bipartite entanglement in a connected network. We showthat genuine multipartite entanglement in a PEN state depends on both the levelof noise and the network topology and, in sharp contrast to the case of purestates, it is not guaranteed by the mere distribution of mixed bipartiteentangled states. Our main result is a markedly drastic feature of thisphenomenon: the amount of connectivity in the network determines whethergenuine multipartite entanglement is robust to noise for any system size orwhether it is completely washed out under the slightest form of noise for asufficiently large number of parties. This latter case implies fundamentallimitations for the application of certain networks in realistic scenarios,where the presence of some form of noise is unavoidable. To illustrate theapplicability of PEN states to study the complex phenomenology behindmultipartite entanglement, we also use them to prove superactivation of genuinemultipartite nonlocality for any number of parties.

Asymptotic survival of genuine multipartite entanglement in noisy quantum networks depends on the topology