Multipartite Entanglement and Hypergraph states of three qubits

TL;DR

This paper classifies hypergraph states of three qubits based on various entanglement measures, revealing their equivalence classes under local transformations and their relation to graph states like the W state.

Contribution

It provides a detailed classification of three-qubit hypergraph states, identifying their equivalence classes under local unitary and stochastic local operations.

Findings

Six classes under local unitary transformations.

Five classes under stochastic local operations with classical communication.

Only one class shares the same entanglement as the W state.

Abstract

Several entanglement measures are used to define equivalence classes in the set of hypergraph states of three qubits. Our classifications reveal that (i) under local unitary transformations, hypergraph states of three qubits are split into six classes and only one class of them is not equivalent to any graph state; (ii) under stochastic local operations with classical communication, for the single copy case hypergraph states of three qubits, partitioned into five classes which can not be converted into a W state, are equivalent to graph states; and (iii) when bipartite entanglement in three qubits considered, hypergraph states of three qubits are split into five classes and only one class of them has the same entangled graph as the W state.