Multipartite entanglement in qudit hypergraph states

We study entanglement properties of hypergraph states in arbitrary finite dimension. We compute multipartite entanglement of elementary qudit hypergraph states, namely those endowed with a single maximum-cardinality hyperedge. We show that, analogously to the qubit case, also for arbitrary dimension there exists a lower bound for multipartite entanglement of connected qudit hypergraph states; this is given by the multipartite entanglement of an equal-dimension elementary hypergraph state featuring the same number of qudits as the largest-cardinality hyperedge. We highlight interesting differences between prime and non-prime dimension in the entanglement features.

Automated summary

We study the entanglement properties of hypergraph states in arbitrary finite dimensions, calculating the multipartite entanglement of elementary qudit hypergraph states. We find that, similar to the qubit case, there exists a lower bound for the multipartite entanglement of connected qudit hypergraph states in arbitrary dimensions. This lower bound is determined by the entanglement of an equal-dimension elementary hypergraph state with the same number of qudits as the largest-cardinality hyperedge. We also observe interesting differences in the entanglement features between prime and non-prime dimensions.