  To any parametric family of states of a finite level quantum system we
associate a space of Fisher maps and introduce the natural notions of
Cram\'er-Rao-Bhattacharya tensor and Fisher information form. This leads us to
an abstract Cram\'er-Rao-Bhattacharya lower bound for the covariance matrix of
any finite number of unbiased estimators of parameteric functions. A number of
illustrative examples is included. Modulo technical assumptions of various
kinds our methods can be applied to infinite level quantum systems as well as
parametric families of classical probability distributions on Borel spaces.
