  Hypergraph states are multiqubit states whose combinatorial description and
entanglement properties generalize the well-studied class of graph states.
Graph states are important in applications such as measurement-based quantum
computation and quantum error correction. The study of hypergraph states, with
their richer multipartite entanglement and other nonlocal properties, has a
promising outlook for new insight into multipartite entanglement. We present
results analyzing local unitary symmetries of hypergraph states, including both
continuous and discrete families of symmetries. In particular, we show how
entanglement types can be detected and distinguished by certain configurations
in the hypergraphs from which hypergraph states are constructed.
