  The fluctuation-dissipation theorem (FDT) is a central result in statistical
physics, both for classical and quantum systems. It establishes a relationship
between the linear response of a system under a time-dependent perturbation and
time correlations of certain observables in equilibrium. Here we derive a
generalization of the theorem which can be applied to any Markov quantum system
and makes use of the symmetric logarithmic derivative (SLD). There are several
important benefits from our approach. First, such a formulation clarifies the
relation between classical and quantum versions of the equilibrium FDT. Second,
and more important, it facilitates the extension of the FDT to arbitrary
quantum Markovian evolutions, as given by quantum maps. Third, it brings out
the full connection between the FDT and the Quantum Fisher information, the
figure of merit in quantum metrology.
