Information geometry and the quantum estimation problem

For the quantum estimation problem only a few of the advanced techniques of classical information geometry have been developed and applied. An asymptotic theory for parameter estimation needs geometric structures which are difficult to construct in the framework of quantum information geometry. It is proposed how a phase-space information geometry can be constructed, which would interpolate between the classical and quantum ones. To motivate this proposal a short review is presented of some current results on estimation and reconstruction of quantum states.