Direct measurement of quantum Fisher information

In the adiabatic perturbation theory, Berry curvature is related to generalized force, and quantum metric tensor linked with energy fluctuation. While former tested numerous numerical results experimental realizations, latter less considered. Quantum Fisher information, key precision measurement, four times tensor. It difficult relate information some physical observable. One interesting candidate square of symmetric logarithmic derivative, which usually tough obtain both theoretically experimentally. The theory enlightens us measure fluctuation directly extract information. this article, we first adopt an alternative way derive link Then numerically testify direct extraction based on in two-level systems simulate realization nitrogen-vacancy center experimentally practical parameters. Statistical models such as transverse field Ising model Heisenberg spin chains are also discussed compare analytical result show level crossing respectively. Our discussion will provide a new scheme benefit measurement understand