  The purpose of the paper is to study the condition for a probability
distribution family to a quantum state family. This is an (relatively) easy
example of quantum version of "comparison of statistical experiments", which
had turned out to supply deep insight into the foundation of classical and
quantum statistics \cite{Strasser}\cite{Torgersen}. It turns out use of maximal
quantum $f$-divergence is useful in characterizing the classical-quantum
transformability.
