# Multiparameter estimation, lower bound on quantum Fisher information and non-Markovianity witnesses of noisy two-qubit systems

## TL;DR

This paper explores quantum Fisher information in noisy two-qubit systems, establishing bounds, witnessing non-Markovianity, and analyzing multiparameter estimation with a focus on quantum coherence and purity.

## Contribution

It introduces new bounds and witnesses for quantum Fisher information and non-Markovianity, and provides analytical formulas for multiparameter estimation in noisy two-qubit systems.

## Key findings

- Quantum interferometric power bounds quantum Fisher information.
- New non-Markovianity witnesses effectively detect memory effects.
- Quantum coherence and purity are crucial for optimal multiparameter estimation.

## Abstract

By using the quantum Fisher information (QFI), we address the process of \textit{single}-parameter estimation in the presence of bosonic as well as fermionic environments and protection of information against the noise. In particular, the quantum interferometric power (IP) of the evolved state of the system is uncovered as an important lower bound for the QFIs of initially encoded parameters. Moreover, we unveil new witnesses of non-Markovianity, that can be used to detect efficiently the memory effects and backflow of information from the environment to the system. On the other hand, we also investigate the \textit{multiparameter} estimation of initial parameters encoded into the quantum state of a two qubit system and obtain analytical formula of the corresponding QFI matrix. In particular, the corresponding quantum Cramer-Rao bounds in both single and multiparameter estimations are analysed. In addition, we illustrate that the quantum \textit{coherence} and \textit{purity} of the evolved state of the probes are two key elements in realizing optimum multiparameter estimation.