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

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