We approach two interconnected problems of quantum information processing in
networks: Conference key agreement and entanglement distillation, both in the
so-called source model where the given resource is a multipartite quantum state
and the players interact over public classical channels to generate the desired
correlation. The first problem is the distillation of a conference key when the
source 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 the
distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local
operations and classical communication (LOCC) from the given mixed state. These
problem settings extend our previous paper [IEEE Trans. Inf. Theory
68(2):976-988, 2022], and we generalise its results: using a quantum version of
the task of communication for omniscience, we derive novel lower bounds on the
distillable conference key from any multipartite quantum state by means of
non-interacting communication protocols. Secondly, we establish novel lower
bounds on the yield of GHZ states from multipartite mixed states. Namely, we
present two methods to produce bipartite entanglement between sufficiently many
nodes so as to produce GHZ states. Next, we show that the conference key
agreement protocol can be made coherent under certain conditions, enabling the
direct generation of multipartite GHZ states