Quantum Hypergraph States

Abstract

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalised stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.

9+5 pages, 5 figures, 1 table, published version

References in corpus (8)

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Universal quantum computation with little entanglement
• Multipartite entanglement in quantum algorithms
• Encoding Hypergraphs into Quantum States
• Scale invariance of entanglement dynamics in Grover's quantum search algorithm
• Purification to Locally Maximally Entangleable States
• Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations
• Multipartite Entanglement and Hypergraph states of three qubits

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