# Optimal and Robust Quantum Metrology Using Interaction-Based Readouts

## TL;DR

This paper demonstrates that interaction-based readout protocols can be designed to achieve both optimal quantum measurement precision and robustness against detection noise, making advanced quantum metrology feasible with current experimental setups.

## Contribution

It proves the flexibility in constructing optimal, noise-robust protocols for quantum metrology using interaction-based readouts, and provides criteria for their implementation.

## Key findings

- Optimal and robust quantum metrology is achievable with current spin-squeezing experiments.
- Full outcome probability distributions enable constructing noise-resistant measurement protocols.
- Interaction-based readouts can be tailored for both optimality and robustness in practical settings.

## Abstract

Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cram{\'e}r-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry \emph{or} to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal \emph{and} robust quantum metrology is achievable in current spin-squeezing experiments.