Direct measurement of quantum Fisher information

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

Automated summary

In the adiabatic perturbation theory, Berry curvature is related to the generalized force, and the quantum metric tensor is linked with energy fluctuation. The direct extraction of the quantum Fisher information based on adiabatic perturbation is numerically tested and experimentally simulated. This practical scheme provides a benefit to quantum precision measurement and a better understanding of the quantum Fisher information.