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

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