LAUSR

We explore quantum multi-parameter estimation, based on quantum Fisher information matrix (QFIM), in an extended anisotropic XY spin chain associated with non-trivial topological characterization driven by varying system parameters (i.e., magnetic field λ, the anisotropic of the nearest-neighbor interaction γ, the next-nearest-neighbor interaction α and its anisotropy δ). The results show that QFIM can provide us a useful tool to detect the topological critical points in this model. Furthermore, we find that the behavior of QFIM associated with variance of estimators are driving parameters dependent at different topological quantum phase transition points. Meanwhile, the choice of estimators $\hat {\theta }$ also take a prominent role on the behavior of QFIM.