Quantum metrology at level anticrossing

We address parameter estimation in two-level systems exhibiting level anticrossing and prove that universally optimal strategies for parameter estimation may be designed. In fact, we find a parameter-independent measurement scheme, leading to the ultimate quantum precision, independently of the value of the parameter of interest. Optimal estimation may be achieved also at high temperature, depending on the structure of the two-level Hamiltonian. Finally, we discuss parameter estimation based on dynamical strategies, and a number of specific applications.

Figure 1

Plot of the function $g_{\lambda }(r_1,r_3)$, corresponding to the ratio between Fisher and quantum Fisher information at zero temperature, for fixed values of $x=\gamma /\mathrm{\Delta }$. The values of $x$ are 0.01, 0.1, 10, 100, going from the top-left to the bottom-right panel. The function is defined only in the region $r_1^2+r_3^2\le 1$. Darker regions correspond to lower values of $g$, from 0 (black) to 1 (white).