Quantum Fisher information of a qubit-qutrit system in Garfinkle–Horowitz–Strominger dilation space–time

We investigate the quantum Fisher information(QFI) of a qubit-qutrit system in the background of Garfinkle–Horowitz–Strominger dilation black hole. After deriving the analytical expression of the QFI, we examine its dynamics with respect to the dilation parameter D and the state parameter γ of the system. Our results show that the QFI for the estimation of γ is a fixed value,which is independent of the parameters D and γ. And the QFI for the estimation of D varies with the parameters D and γ. Additionally, we propose an effective strategy to steer the QFI by introducing weak measurement reversal. We find that the QFI can be remarkably enhanced by adjusting the appropriate reversing measurement strengths. Our findings might provide some useful insights for the study on parameter estimation of hybrid systems in the framework of relativity theory.