  The subject of this paper is a mathematical transition from the Fisher
information of classical statistics to the matrix formalism of quantum theory.
If the monotonicity is the main requirement, then there are several quantum
versions parametrized by a function. In physical applications the minimal is
the most popular. There is a one-to-one correspondence between Fisher
informations (called also monotone metrics) and abstract covariances. The skew
information and the chi-square-divergence are treated here as particular cases.
