  Hypergraph states form a family of multiparticle quantum states that
generalizes the well-known concept of Greenberger-Horne-Zeilinger states,
cluster states, and more broadly graph states. We study the nonlocal properties
of quantum hypergraph states. We demonstrate that the correlations in
hypergraph states can be used to derive various types of nonlocality proofs,
including Hardy-type arguments and Bell inequalities for genuine multiparticle
nonlocality. Moreover, we show that hypergraph states allow for an
exponentially increasing violation of local realism which is robust against
loss of particles. Our results suggest that certain classes of hypergraph
states are novel resources for quantum metrology and measurement-based quantum
computation.
