Multipartite entanglement in qudit hypergraph states

TL;DR

This paper investigates the entanglement properties of hypergraph states in finite-dimensional qudits, establishing bounds and highlighting differences between prime and non-prime dimensions.

Contribution

It introduces a lower bound for multipartite entanglement in qudit hypergraph states and compares entanglement features across different dimensions.

Findings

Lower bound for entanglement in connected qudit hypergraph states

Entanglement differences between prime and non-prime dimensions

Comparison with qubit hypergraph states

Abstract

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.