  The aim of the present paper is to give axiomatic characterization of quantum
relative entropy utilizing resource conversion scenario. We consider two sets
of axioms: non-asymptotic and asymptotic. In the former setting, we prove that
the upperbound and the lowerbund of D^{Q}({\rho}||{\sigma}) is
D^{R}({\rho}||{\sigma}):=tr{\rho}ln{\sigma}^{1/2}{\rho}^{-1}{\sigma}^{1/2} and
D({\rho}||{\sigma}):= tr{\rho}(ln{\rho}-ln{\sigma}), respectively. In the
latter setting, we prove uniqueness of quantum relative entropy, that is,
D^{Q}({\rho}||{\sigma}) should equal a constant multiple of
D({\rho}||{\sigma}). In the analysis, we define and use reverse test and
asymptotic reverse test, which are natural inverse of hypothesis test.
