  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 $\mathrm{D}^{Q}(\rho||\sigma) $ is
$\mathrm{D}^{R}(\rho||\sigma) :=\mathrm{tr}%
\,\rho\ln\sqrt{\rho}\sigma^{-1}\sqrt{\rho}$ and $\mathrm{D}(\rho||\sigma) :=$
$\mathrm{tr}\,\rho(\ln\rho-\ln\sigma) $, respectively. In the latter setting,
we prove uniqueness of quantum relative entropy, that is,
$\mathrm{D}^{Q}(\rho||\sigma) $ should equal a constant multiple of
$\mathrm{D}(\rho||\sigma) $. In the analysis, we define and use reverse test
and asymptotic reverse test, which are natural inverse of hypothesis test.
