The results of local measurements on some composite quantum systems cannot be
reproduced classically. This impossibility, known as quantum nonlocality,
represents a milestone in the foundations of quantum theory. Quantum
nonlocality is also a valuable resource for information processing tasks, e.g.
quantum communication, quantum key distribution, quantum state estimation, or
randomness extraction. Still, deciding if a quantum state is nonlocal remains a
challenging problem. Here we introduce a novel approach to this question: we
study the nonlocal properties of quantum states when distributed and measured
in networks. Using our framework, we show how any one-way entanglement
distillable state leads to nonlocal correlations. Then, we prove that
nonlocality is a non-additive resource, which can be activated. There exist
states, local at the single-copy level, that become nonlocal when taking
several copies of it. Our results imply that the nonlocality of quantum states
strongly depends on the measurement context.Comment: 4 + 3 pages, 4 figure