Non-Hermitian-assisted enhancement precision of parameter estimation

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.