  We derive a necessary and sufficient condition for a sequence of quantum
measurements to achieve the optimal performance in quantum hypothesis testing.
Using an information-spectrum method, we discuss what quantum measurement we
should perform in order to attain the optimal exponent of the second error
probability under the condition that the first error probability goes to 0. As
an asymptotically optimal measurement, we propose a projection measurement
characterized by the irreducible representation theory of the special linear
group SL(H). Specially, in spin 1/2 system, it is realized by the simultaneous
measurement of the total momentum and a momentum of a specified direction. As a
byproduct, we obtain another proof of quantum Stein's lemma.
