Qudit hypergraph states

Abstract

We generalize the class of hypergraph states to multipartite systems of qudits, by means of constructions based on the $d$-dimensional Pauli group and its normalizer. For simple hypergraphs, the different equivalence classes under local operations are shown to be governed by a greatest-common-divisor hierarchy. Moreover, the special cases of three qutrits and three ququarts is analyzed in detail.