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Quantum hypergraph states are the natural generalization of graph states.Here we investigate and analytically quantify entanglement and nonlocality forlarge classes of quantum hypergraph states. More specifically, we connect thegeometric measure of entanglement of symmetric hypergraphs to their local Paulistabilizers. As a result we recognize the resemblance between symmetric graphstates and symmetric hypergraph states, which explains both, exponentiallyincreasing violation of local realism for infinitely many classes of hypergraphstates and its robustness towards particle loss.

Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality