# Optimal joint estimation of multiple Rabi frequencies

## TL;DR

This paper investigates the optimal methods for simultaneously estimating multiple Rabi frequencies in a multilevel quantum system, revealing conditions where joint estimation outperforms separate estimation and how adaptive controls can enhance this advantage.

## Contribution

It analytically determines the optimal probe states and measurements for joint estimation, and explores the regimes where joint estimation is advantageous or not.

## Key findings

- Joint estimation can outperform separate estimation in certain regimes.
- Adaptive quantum controls can restore the advantage of joint estimation.
- The highest precision limits are analytically derived.

## Abstract

We study the joint estimation of multiple Rabi frequencies in a multilevel system. By analytically identifying the optimal probe state and the optimal measurement, we obtain the highest precision limit for the joint estimation of multiple Rabi frequencies. We show that the joint estimation does not always outperform the separate estimation. In different regimes the joint estimation can either outperform or underperform the separate estimation. We further show that if additional adaptive quantum controls are allowed then the advantage of the joint estimation over the separate estimation can be reestablished.