  The tomographic picture of quantum mechanics has brought the description of
quantum states closer to that of classical probability and statistics. On the
other hand, the geometrical formulation of quantum mechanics introduces a
metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure
states. By putting these two aspects together, we show that the Fisher
information metric, both classical and quantum, can be described by means of
the Hermitian tensor on the manifold of pure states.
