Graphical description of unitary transformations on hypergraph states

Abstract

Hypergraph states form a family of multiparticle quantum states that generalizes cluster states and graph states. We study the action and graphical representation of nonlocal unitary transformations between hypergraph states. This leads to a generalization of local complementation and graphical rules for various gates, such as the CNOT gate and the Toffoli gate. As an application, we show that already for five qubits local Pauli operations are not sufficient to check local equivalence of hypergraph states. Furthermore, we use our rules to construct entanglement witnesses for three-uniform hypergraph states.

17 pages, 5 figures, v2: final version

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• Entanglement detection
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• Entanglement and nonclassical properties of hypergraph states
• Encoding Hypergraphs into Quantum States
• Multipartite entanglement detection for hypergraph states
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Cited by in corpus (10)

• Error protected qubits in a silicon photonic chip
• Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states
• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• Hypergraph Simplification: Linking the Path-sum Approach to the ZH-calculus
• Entanglement of random hypergraph states
• Analysis of quantum error correction with symmetric hypergraph states
• Local Pauli stabilizers of symmetric hypergraph states
• Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality
• Entanglement Purification of Hypergraph States
• Graphical Framework for Non-Gaussian Quantum States