On error exponents in quantum hypothesis testing

Author

Ogawa, Tomohiro ; Hayashi, Masahito

Author_Institution

Dept. of Math. Informatics, Univ. of Tokyo, Japan

Volume

50

Issue

6

fYear

2004

fDate

6/1/2004 12:00:00 AM

Firstpage

1368

Lastpage

1372

Abstract

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.

Keywords

Hilbert spaces; entropy; error statistics; information theory; mathematical operators; quantum theory; Hoeffding bound noncommutative analog; density operator; error exponent; error probability; key operator inequality; quantum Stein lemma; quantum hypothesis testing; quantum information theory; quantum relative entropy; Channel coding; Educational technology; Entropy; Error probability; Information theory; Probability distribution; Quantum computing; Quantum mechanics; Testing; Upper bound; Error exponent; Hoeffding bound; hypothesis testing; quantum Stein's lemma; quantum relative entropy;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2004.828155

Filename

1302320