1999/06/24 by Tomohiro Ogawa, Hiroshi Nagaoka · 5 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1142/9789812563071_0003
LaTeX, 12 pages, submitted to IEEE Trans. Inform. Theory
arxiv created 1999/06/24 · arxiv updated 2016/11/18
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.