The precision of parameter estimation for dephasing model under squeezed reservoir

Abstract

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