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Strong converse and Stein's lemma in quantum hypothesis testing

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2 Author(s)
Ogawa, T. ; Dept. of Math. Eng. & Inf. Phys., Tokyo Univ., Japan ; Nagaoka, H.

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, which complements the result of Hiai and Petz (1991) to establish the quantum version of Stein's lemma. The inequality is also used to show a bound on the probability of errors of the first kind when the power exponent for the probability of errors of the second kind exceeds the quantum relative entropy, which yields the strong converse in quantum hypothesis testing. Finally, we discuss the relation between the bound and the power exponent derived by Han and Kobayashi (1989) in classical hypothesis testing

Published in:

Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 7 )

Date of Publication:

Nov 2000

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