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We approach two interconnected problems of quantum information processing innetworks: Conference key agreement and entanglement distillation, both in theso-called source model where the given resource is a multipartite quantum stateand the players interact over public classical channels to generate the desiredcorrelation. The first problem is the distillation of a conference key when thesource state is shared between a number of legal players and an eavesdropper;the eavesdropper, apart from starting off with this quantum side information,also observes the public communication between the players. The second is thedistillation of Greenberger-Horne-Zeilinger (GHZ) states by means of localoperations and classical communication (LOCC) from the given mixed state. Theseproblem settings extend our previous paper [IEEE Trans. Inf. Theory68(2):976-988, 2022], and we generalise its results: using a quantum version ofthe task of communication for omniscience, we derive novel lower bounds on thedistillable conference key from any multipartite quantum state by means ofnon-interacting communication protocols. Secondly, we establish novel lowerbounds on the yield of GHZ states from multipartite mixed states. Namely, wepresent two methods to produce bipartite entanglement between sufficiently manynodes so as to produce GHZ states. Next, we show that the conference keyagreement protocol can be made coherent under certain conditions, enabling thedirect generation of multipartite GHZ states.

New Protocols for Conference Key and Multipartite Entanglement Distillation