Strong converse and Stein's lemma in quantum hypothesis testing

The hypothesis testing problem for two quantum states is treated. We show a new inequality between the errors of the first kind and the second kind, w hich complements the result of Hiai and Petz to establish the quantum versi on of Stein's lemma. The inequality is also used to show a bound on the pro bability of errors of the first kind when the power exponent for the probab ility of errors of the second kind exceeds the quantum relative entropy, wh ich yields the strong converse in quantum hypothesis testing. Finally, we d iscuss the relation between the bound and the power exponent derived by Han and Kobayashi in classical hypothesis testing.