  Beyond future applications, quantum networks open interesting fundamental
perspectives, notably novel forms of quantum correlations. In this work we
discuss quantum correlations in networks from the perspective of the underlying
quantum states and their entanglement. We address the questions of which states
can be prepared in the so-called triangle network, consisting of three nodes
connected pairwise by three sources. We derive necessary criteria for a state
to be preparable in such a network, considering both the cases where the
sources are statistically independent and classically correlated. This shows
that the network structure imposes strong and non-trivial constraints on the
set of preparable states, fundamentally different from the standard
characterization of multipartite quantum entanglement.
