  The hypothesis testing problem of two quantum states is treated. We show a
new inequality between the error of the first kind and the second kind, which
complements the result of Hiai and Petz to establish the quantum version of
Stein's lemma. The inequality is also used to show a bound on the first kind
error when the power exponent for the second kind error exceeds the quantum
relative entropy, and the bound yields the strong converse in the quantum
hypothesis testing. Finally, we discuss the relation between the bound and the
power exponent derived by Han and Kobayashi in the classical hypothesis
testing.
