# Adaptive quantum metrology under general Markovian noise

## TL;DR

This paper analyzes the fundamental limits of quantum parameter estimation under Markovian noise, establishing conditions for precision scaling and exploring error correction to restore optimal performance, with applications to atomic interferometry.

## Contribution

It provides an algebraic condition determining when the Heisenberg limit can be achieved under Markovian noise and discusses protocols to recover optimal scaling.

## Key findings

- Precision scales at most as 1/√T under general Markovian noise.
- Conditions are identified for restoring 1/T scaling via error correction.
- Application to atomic interferometry reveals new insights into non-linear metrological limits.

## Abstract

We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated with precision scaling as $1/T$, where $T$ is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum Master equation, implying at most $1/\sqrt{T}$ scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction like protocol must satisfy in order to regain the $1/T$ precision scaling in case the above mentioned algebraic condition is not satisfied. Furthermore, we apply the developed methods to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of non-linear metrological models.