# Connecting measurement invasiveness to optimal metrological scenarios

## TL;DR

This paper explores how measurement invasiveness, quantified by the Leggett-Garg inequality violation, relates to optimal quantum metrological scenarios through Fisher information, highlighting a link between quantum correlations and measurement precision.

## Contribution

It establishes a connection between quantum temporal correlations and Fisher information, linking measurement invasiveness to metrological performance in both perfect and noisy measurements.

## Key findings

- High Fisher information scenarios correlate with Leggett-Garg inequality violation.
- Quantum temporal correlations can be expressed in terms of Fisher information.
- Measurement invasiveness impacts quantum metrological efficiency.

## Abstract

The connection between the Leggett-Garg inequality and optimal scenarios from the point of view of quantum metrology is investigated for perfect and noisy general dichotomic measurements. In this context, we show that the Fisher information can be expressed in terms of quantum temporal correlations. This connection allows us to associate scenarios with relatively high Fisher information to scenarios in which the Leggett-Garg inequality is violated. We thus demonstrate a qualitative and, to some extent, quantitative link between measurement invasiveness and metrological performance. Finally, we illustrate our results by using a specific model for spin systems.