Direct measurement of quantum Fisher information

TL;DR

This paper proposes a practical method to directly measure quantum Fisher information through energy fluctuations, supported by numerical simulations and experimental proposals, advancing quantum precision measurement techniques.

Contribution

It introduces an alternative derivation linking energy fluctuation to quantum Fisher information and demonstrates its experimental feasibility in various quantum systems.

Findings

Successful numerical extraction of quantum Fisher information in two-level systems

Simulation of experimental realization in nitrogen-vacancy centers

Comparison with statistical models like Ising and Heisenberg chains

Abstract

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, key to quantum precision measurement, is four times quantum metric tensor. It is difficult to relate the quantum Fisher information with some physical observable. One interesting candidate is 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 the direct extraction of the quantum Fisher information based on adiabatic perturbation in two-level systems and simulate the experimental realization in nitrogen-vacancy center with experimentally practical parameters. Statistical models such as 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 new practical scheme to measure the quantum Fisher information, and will also benefit the quantum precision measurement and the understand of the quantum Fisher information.