Quantum Fisher information of a two-level system controlled by non-Hermitian operation under depolarization

We investigated the dynamics of quantum Fisher information for a two-level system controlled by a non-Hermitian operation under the depolarization, and the non-Hermitian operation is described by a special Hamiltonian in which both the PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {PT}$$\end{document}-symmetric zone and the PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {PT}$$\end{document}-symmetry broken zone are considered. Our results show that the non-Hermitian operation can effectively control the evolutionary behavior of quantum Fisher information of the system. Especially, through a proper choice of the non-Hermiticity parameter combining with the optimal input state and a low depolarizing probability, quantum Fisher information of the system can be significantly increased by the non-Hermitian operation. According to the quantum Cramér–Rao inequality, the inverse of quantum Fisher information provides the lower bound of the error of the parameter estimation. Our investigation also shows that the non-Hermiticity in the operation which is performed on the initial state is robust against the depolarizing decoherence, and the precision of parameter estimation can be remarkably enhanced by applying an appropriate non-Hermitian operation.