Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 50, Issue 6, Pages 1368-1372Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2004.828155
Keywords
error exponent; Hoeffding bound; hypothesis testing; quantum relative entropy; quantum Stein's lemma
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In the simple quantum hypothesis testing problem for two density operators, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and a conditional expectation of it. Concerning the error exponents, the upper bounds lead to a noncommutative analog of the Hoeffding bound, which is identical with the classical counterpart if two density operators commute. The upper bounds also provide a simple proof of the direct part of the quantum Stein's lemma.
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