Lee-Yang zeros and quantum Fisher information matrix in a nonlinear system

The distribution of Lee-Yang zeros not only matters in thermodynamics and quantum mechanics, but also mathematics. Hereby we propose a nonlinear toy model discuss the corresponding zeros. Utilizing coupling between probe qubit system, all can be detected dynamics by tuning strength linear coefficient system. Moreover, analytical expression Fisher information matrix at is provided an interesting phenomenon discovered. Both temperature simultaneously attain their precision limits However, cannot work as thermometer zero if it sits on unit circle.