A new approach to the Cramer-Rao type bound of the pure state model

In this paper, new methodology – direct approach – for the determination of the attainable CR type bound of the pure state model, is proposed and successfully applied to the wide variety of pure state models, for example, the 2-dimensional arbitrary model, the coherent model with arbitrary dimension. When the weight matrix is SLD Fisher information, the bound is determined for arbitrary pure state models. Manifestation of complex structure in the Cramer-Rao type bound is also discussed.