On Error Exponents in Quantum Hypothesis Testing

Tomohiro Ogawa; Masahito Hayashi

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On Error Exponents in Quantum Hypothesis Testing

Tomohiro Ogawa·Masahito Hayashi

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Abstract

In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a noncommutative analogue of the Hoeffding bound, which is identical with the classical counter part if the hypotheses, composed of two density operators, are mutually commutative. The upper bounds also provide a simple proof of the direct part of the quantum Stein's lemma.

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Tomohiro Ogawa, Masahito Hayashi. 2002-08-14. On Error Exponents in Quantum Hypothesis Testing. https://arxiv.org/abs/quant-ph/0206151

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