The precision of parameter estimation for dephasing model under squeezed reservoir

We study the precision of parameter estimation for dephasing model under squeezed environment. We analytically calculate the dephasing factor $\gamma(t)$ and obtain the analytic quantum Fisher information (QFI) for the amplitude parameter $\alpha$ and the phase parameter $\phi$. It is shown that the QFI for the amplitude parameter $\alpha$ is invariant in the whole process, while the QFI for the phase parameter $\phi$ strongly depends on the reservoir squeezing. It is shown that the QFI can be enhanced for appropriate squeeze parameters $r$ and $\theta$. Finally, we also investigate the effect of temperature on the QFI.