Local unitary symmetries of hypergraph states

TL;DR

This paper investigates the local unitary symmetries of hypergraph states, revealing how their entanglement types can be identified through hypergraph configurations, advancing understanding of multipartite entanglement.

Contribution

It provides a detailed analysis of continuous and discrete local unitary symmetries in hypergraph states, linking hypergraph structures to entanglement classification.

Findings

Identification of symmetry types in hypergraph states

Connection between hypergraph configurations and entanglement properties

Enhanced understanding of multipartite entanglement structure

Abstract

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.