Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this Letter 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 cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and nontrivial constraints on the set of preparable states, fundamentally different from the standard characterization of multipartite quantum entanglement.

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• Nonlocality
• Quantum communication
• Quantum entanglement
• Quantum networks