Detecting metrologically useful entanglement in the vicinity of Dicke states

TL;DR

The paper introduces a method to verify the metrological usefulness of noisy Dicke states using minimal collective measurements, enabling detection of entanglement beneficial for quantum sensing without direct sensitivity measurement.

Contribution

It provides a practical approach to assess the usefulness of Dicke states for quantum metrology with limited measurements, applicable to experimental data.

Findings

Method successfully verifies metrological usefulness of noisy Dicke states.

Applicable to recent experimental results for entanglement detection.

Reduces measurement complexity for quantum metrology validation.

Abstract

We present a method to verify the metrological usefulness of noisy Dicke states of a particle ensemble with only a few collective measurements, without the need for a direct measurement of the sensitivity. Our method determines the usefulness of the state for the usual protocol for estimating the angle of rotation with Dicke states, which is based on the measurement of the second moment of a total spin component. It can also be used to detect entangled states that are useful for quantum metrology. We test our approach on recent experimental results.