Qudit Hypergraph States

TL;DR

This paper extends hypergraph states to systems of qudits, exploring their classification under local operations and analyzing specific cases like three qutrits and ququarts.

Contribution

It introduces a generalization of hypergraph states to qudits using the d-dimensional Pauli group and studies their equivalence classes and special cases.

Findings

Equivalence classes are governed by a greatest common divisor hierarchy.

Detailed analysis of three qutrits and three ququarts cases.

Framework for classifying 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 analysed in detail.