Entanglement and nonclassical properties of hypergraph states (Q2878649)

The paper deals with entanglement properties and nonclassical features of hypergraph states. A hypergraph allows that an edge is connected to any number of vertices, so there are also edges with three, four, or more vertices. Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states. The entangleable states can be described elegantly and in a compact form by a hypergraph that indicates a possible generation procedure of these states. Two states that are connected with a local unitary transformation are called locally equivalent. The local unitary equivalence classes up to four-qubits are described, as well as important classes of five- and six-qubit states with their entanglement properties. It is shown that the properties of the hypergraph remain invariant under local Pauli operators, so they can be used to distinguish equivalence classes. Finally it is shown that the stabilizer formalism of hypergraph states that exploits the Pauli operators can be used to derive various inequalities for testing the Kochen-Specker theorem or Bell's theorem.