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Local Unitary Symmetries of Hypergraph States

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Hypergraph states are multi-qubit 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 compared to the graph states, has a promising outlook for new insight into multipartite entanglement. We report on recent results applying an analysis of local unitary symmetry to graph and hypergraph states. In particular, we show how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed. By way of introduction, we present a brief survey of the method and results on local unitary entanglement classification using an analysis of local unitary symmetry.

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