Determining the Continuous Family of Quantum Fisher Information from Linear Response Theory

TL;DR

This paper demonstrates that the entire quantum Fisher information family can be obtained from linear response theory via generalized covariances, linking fundamental quantum limits to measurable response functions.

Contribution

It introduces a method to determine the quantum Fisher information from linear response functions using a generalized fluctuation-dissipation theorem.

Findings

Derived the generalized fluctuation-dissipation theorem.

Showed quantum Fisher information can be experimentally measured.

Validated the approach with a harmonic oscillator example.

Abstract

The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher information can be determined from linear response theory through generalized covariances. We derive the generalized fluctuation-dissipation theorem that relates the linear response function to generalized covariances and hence allows us to determine the quantum Fisher information from linear response functions, which is experimentally measurable quantities. As an application, we examine the skew information, which is one of the quantum Fisher information, of a harmonic oscillator in thermal equilibrium, and show that the equality of the skew information-based uncertainty relation holds.