  Recently, Zhong et al. [Phys. Rev. A 87, 022337(2013)] investigated the
dynamics of quantum Fisher information (QFI) in the presence of decoherence. We
here reform their results and propose two schemes to enhance and preserve the
QFIs for a qubit system subjected to a decoherence noisy environment by
applying $\textit{non-Hermitian}$ operators process. The proposed schemes are
related to the $\textit{prior}$ (or the $\textit{post}$ ) non-Hermitian
operator process corresponding to before (or after) the interest system suffers
from decoherence, respectively. Resorting to the Bloch sphere representation,
we derive the exact analytical expressions of the QFIs with respect to the
amplitude parameter $\theta$ and the phase parameter $\phi$, and in detail
investigate the influence of $\textit{non-Hermitian}$ operator parameters on
the QFIs. Compared with purity decoherence process (without non-Hermitian
operator process), we find that the $\textit{post non-Hermitian}$ operator
process can potentially enhance and preserve the QFIs by choosing appropriate
$\textit{non-Hermitian}$ operator parameters, while with the help of the
$\textit{prior non-Hermitian}$ operator process one could completely eliminate
the effect of decoherence to improve the parameters estimation. Finally, a
generalized non-Hermitian operator parameters effect on the parameters
estimation is also considered.
