Abstract
•The quantum Fisher information matrix (QFIM) is used to find the optimal state induced from the twisting model at thermal temperature.•There are three main parameters describe the optimal states; the strength of the transverse field and the squeezing interaction parameters in addition to the temperature.•The minimum variances of each two parameters are estimated simultaneously and individually.•The quantum Fisher information matrix gives a good indicator of estimating the parameters which describe the optimal state.•Estimating each pair simultaneously is much better than individual estimation.
The possibility of estimating parameters and describing the optimal states induced from the one-axis twisting model on the thermal state was examined. The quantum Fisher information matrix be used as an estimator for multiple parameters. We demonstrate that concurrent estimation reduces estimation of parameter variance, and therefore the precision of estimating parameters simultaneously is much better than estimating them individually. Saturation is imaged at significant temperatures, although it increases the minimum variations in reaction force. It is shown that each parameter can be used as a control parameter to reduce the minimum variances for other parameters.