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 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 cannot be converted into a
W state, are equivalent to graph states; and (iii) when bipartite entanglement in three qubits is considered, hypergraph states of three qubits are split into five classes and only one of them has the same entangled graph as the
W state.
Abstract As quantum computing technology slowly matures and the number of available qubits on a QPU gradually increases, interest in assessing the capabilities of quantum computing hardware in a scalable manner is growing. One of the key properties for quantum computing is the ability to generate multipartite entangled states. In this study, aspects of benchmarking entanglement generation capabilities of noisy intermediate‐scale quantum (NISQ) devices are discussed based on the preparation of graph states and the verification of entanglement in the prepared states. Thereby, entanglement witnesses that are specifically suited for a scalable experiment design are used. This choice of entanglement witnesses can detect A) bipartite entanglement and B) genuine multipartite entanglement for graph states with constant two measurement settings if the prepared graph state is based on a two‐colorable graph, e.g., a square grid graph or one of its subgraphs. With this, it is experimentally verified that a bipartite entangled state comprising all qubits can be prepared on a 127‐qubit IBM Quantum superconducting QPU, and genuine multipartite entanglement can be detected for states of up to 23 qubits with quantum readout error mitigation.
In quantum information theory, maximally entangled states, specifically locally maximally entangled (LME) states, are essential for quantum protocols. While many focus on bipartite entanglement, applications such as quantum error correction and multiparty secret sharing rely on multipartite entanglement. These LME states naturally appear in the invariant subspaces of tensor products of irreducible representations of the symmetric group
Sn, called Kronecker subspaces, whose dimensions are the Kronecker coefficients. A Kronecker subspace is a space of multipartite LME states that entangle high-dimensional Hilbert spaces. Although these states can be derived from Clebsch-Gordan coefficients of
Sn, known methods are inefficient even for small
n. A quantum-information-based alternative comes from entanglement concentration protocols, where Kronecker subspaces arise in the isotypic decomposition of multiple copies of entangled states. Closed forms have been found for the multiqubit
W-class states, but not in general. This thesis extends that approach to any multiqubit system. We first propose a graphical construction called W-state Stitching, where multiqubit entangled states are represented as tensor networks built from
W states. By analyzing the isotypic decomposition of copies of these graph states, corresponding graph Kronecker states can be constructed. In particular, graph states of generic multiqubit systems can generate any Kronecker subspace. We explicitly construct bases for three- and four-qubit systems and show that the W-stitching technique also serves as a valuable tool for multiqubit entanglement classification. These results may open new directions in multipartite entanglement resource theories, with bipartite and tripartite
W states as foundational elements, and asymptotic analysis based on Kronecker states.