A New Proof of the Direct Part of Stein's Lemma in Quantum Hypothesis Testing

Tomohiro Ogawa; Masahito Hayashi

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A New Proof of the Direct Part of Stein's Lemma in Quantum Hypothesis Testing

Tomohiro Ogawa·Masahito Hayashi

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Abstract

The direct part of Stein's lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein's lemma without using Hiai-Petz's theorem, along with an operator monotone function, and in addition it is also used to show a new proof of Hiai-Petz's theorem.

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Tomohiro Ogawa, Masahito Hayashi. 2001-10-21. A New Proof of the Direct Part of Stein's Lemma in Quantum Hypothesis Testing. https://arxiv.org/abs/quant-ph/0110125

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