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Efficient Verification of Hypergraph States
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Graph states and hypergraph states are of wide interest in quantum information processing and foundational studies. Efficient verification of these states is a key to various applications. Here we propose a simple method for verifying hypergraph states which requires only two distinct Pauli measurements for each party, yet its efficiency is comparable to the best strategy based on entangling measurements. For a given state, the overhead is bounded by the chromatic number and degree of the underlying hypergraph. Our protocol is dramatically more efficient than all previous protocols based on local measurements, including tomography and direct fidelity estimation. It enables the verification of hypergraph states and genuine multipartite entanglement of thousands of qubits. The protocol can also be generalized to the adversarial scenario, while achieving almost the same efficiency. This merit is particularly appealing to demonstrating blind measurement-based quantum computation and quantum supremacy.
Forward citations
Cited by 4 Pith papers
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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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Efficient certification of intractable quantum states with few Pauli measurements
The paper claims Clifford-enhanced product states can be certified with O(n^2/epsilon^2) Pauli measurements in the i.i.d. setting and polynomially many in the adversarial setting, but the central estimator is derived ...
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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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