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Quantum Hypergraph States
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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.
Forward citations
Cited by 7 Pith papers
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Genuine Multipartite Entanglement between Logical Qubits via Cross-Code Lattice Surgery
Cross-code lattice surgery between surface and 3D colour codes yields certified logical GHZ and |CCZ> GME plus arbitrary logical rotations on a trapped-ion processor.
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Graph restricted tensors: building blocks for holographic networks
Graph-restricted tensors generalize 1-uniform states, dual-unitary operators and AME states, with exact analytic solutions for new examples motivated by holographic lattice models.
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Device-Independent Self-Testing of the Three-Qubit CCZ Hypergraph State
The CCZ hypergraph state and its Pauli measurements can be device-independently self-tested from twenty correlators, and also from maximal violation of a specially constructed Bell inequality.
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Magic-protected entanglement and Clifford-irreducible structure in magic state space
Quantum states are classified by how much bipartite entanglement survives optimal simplification by classically easy Clifford operations, yielding a split into weakly protected T-magic and strongly protected W-magic regimes.
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Calibrated hypergraph states: II calibrated hypergraph state construction and applications
Calibrated hypergraph states over Galois rings generalize weighted hypergraph states, are stabilizer and locally maximally entangleable, and reduce to the weighted class in the qubit case only.
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Calibrated hypergraph states: I calibrated hypergraph and multi qudit state monads
Calibrated hypergraphs and multi-qudit states are shown to form graded Ω monads, providing a categorical foundation for a broad generalization of hypergraph states.
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Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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