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.