  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.
