Entanglement and nonlocality of four-qubit connected hypergraph states

We study entanglement and nonlocality of connected four-qubit hypergraph states. One obtains the Stochastic Local Operations and Classical Communication (SLOCC) classification from the known local unitary (LU)-orbits. We then consider Mermin's polynomials and show that the nonlocal behavior of hypergraph states can be detected by a suitable choice of Mermin's inequality. Finally, we implement some of the corresponding inequalities on the IBM Quantum Experience and report the detection of the nonlocality of a three-qubit hypergraph states.