dorsal/arxiv
View SchemaQuantum Stein's lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb
| Authors | Igor Bjelakovic, Rainer Siegmund-Schultze |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307170 |
| URL | https://arxiv.org/abs/quant-ph/0307170 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large numbers only. Joint convexity of the quantum relative entropy is proven too, resulting in a self-contained elementary version of Tropp's approach to Lieb's concavity theorem, according to which the map tr(exp(h+log a)) is concave in a on positive operators for self-adjoint h.
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"date_created": "2026-03-02T18:01:59.541000Z",
"date_modified": "2026-03-02T18:01:59.541000Z",
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"abstract": "We derive the monotonicity of the quantum relative entropy by an elementary\noperational argument based on Stein\u0027s lemma in quantum hypothesis testing. For\nthe latter we present an elementary and short proof that requires the law of\nlarge numbers only. Joint convexity of the quantum relative entropy is proven\ntoo, resulting in a self-contained elementary version of Tropp\u0027s approach to\nLieb\u0027s concavity theorem, according to which the map tr(exp(h+log a)) is\nconcave in a on positive operators for self-adjoint h.",
"arxiv_id": "quant-ph/0307170",
"authors": [
"Igor Bjelakovic",
"Rainer Siegmund-Schultze"
],
"categories": [
"quant-ph",
"cs.IT",
"math-ph",
"math.IT",
"math.MP"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Quantum Stein\u0027s lemma revisited, inequalities for quantum entropies, and a concavity theorem of Lieb",
"url": "https://arxiv.org/abs/quant-ph/0307170"
},
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"execution_id": "0bf8de6b-29d2-47a2-90ef-ed9dbc86f9dd",
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