Efficient Verification of Hypergraph States

TL;DR

This paper introduces a simple, efficient method for verifying hypergraph states in quantum information, requiring minimal measurements and enabling verification of large-scale entangled states with high efficiency.

Contribution

A novel verification protocol for hypergraph states using only two Pauli measurements per party, matching the efficiency of entangling measurement strategies.

Findings

Requires only two Pauli measurements per party

Achieves efficiency comparable to entangling measurement strategies

Enables verification of thousands of qubits and genuine multipartite entanglement

Abstract

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.