# Efficient verification of Dicke states

## TL;DR

This paper introduces highly efficient, practical protocols for verifying large Dicke states in quantum systems, significantly reducing the number of measurements needed compared to previous methods.

## Contribution

The authors develop adaptive and nonadaptive verification protocols for Dicke states requiring only two measurement settings, with exponential efficiency improvements over prior local measurement techniques.

## Key findings

- Verification requires only O(nε^{-1}lnδ^{-1}) tests.
- Protocols are applicable to hundreds of qubits with current technology.
- Performance matches the best global strategies in efficiency.

## Abstract

Among various multipartite entangled states, Dicke states stand out because their entanglement is maximally persistent and robust under particle losses. Although much attention has been attracted for their potential applications in quantum information processing and foundational studies, the characterization of Dicke states remains as a challenging task in experiments. Here, we propose efficient and practical protocols for verifying arbitrary $n$-qubit Dicke states in both adaptive and nonadaptive ways. Our protocols require only two distinct settings based on Pauli measurements besides permutations of the qubits. To achieve infidelity $\epsilon$ and confidence level $1-\delta$, the total number of tests required is only $O(n\epsilon^{-1}\ln\delta^{-1})$. This performance is exponentially more efficient than all previous protocols based on local measurements, including quantum state tomography and direct fidelity estimation, and is comparable to the best global strategy. Our protocols are readily applicable with current experimental techniques and are able to verify Dicke states of hundreds of qubits.