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Multipartite Hypergraph Centralizer and normalizer Mathematics Equivalence (formal languages) Simple (philosophy) Combinatorics Hierarchy Class (philosophy) Discrete mathematics Computer science Physics Law Quantum Quantum mechanics Political science Epistemology Philosophy Artificial intelligence Quantum entanglement

F. E. S. Steinhoff , Christina Ritz , Nikolai Miklin , Otfried Gühne ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.1103/physreva.95.052340 · OA: W2580150930

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.