LIPIcs.TQC.2014.88.pdf
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Convexity Properties of the Quantum Rényi Divergences, with Applications to the Quantum Stein's Lemma
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9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2014-12-11
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Milán Mosonyi. Convexity Properties of the Quantum Rényi Divergences, with Applications to the Quantum Stein's Lemma. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 88-98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.TQC.2014.88
https://doi.org/10.4230/LIPIcs.TQC.2014.88
Abstract
We show finite-size bounds on the deviation of the optimal type II error from its asymptotic value in the quantum hypothesis testing problem of Stein's lemma with composite null-hypothesis.
The proof is based on some simple properties of a new notion of quantum Rènyi divergence, recently introduced in [Müller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013)], and [Wilde, Winter, Yang, arXiv:1306.1586].
Keywords
- Quantum Rényi divergences
- Stein's lemma
- composite null-hypothesis
- second-order asymptotics
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