Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality

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