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Convexity properties of the quantum Rényi divergences, with applications to the quantum Stein’s lemma. (English) Zbl 1359.81069

Flammia, Steven T. (ed.) et al., 9th conference on the theory of quantum computation, communication and cryptography, TQC 2014, Singapore, May 21–23, 2014. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-73-6). LIPIcs – Leibniz International Proceedings in Informatics 27, 88-98 (2014).
Summary: 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 Rényi divergence, recently introduced in [M. Müller-Lennert et al., J. Math. Phys. 54, No. 12, 122203, 20 p. (2013; Zbl 1290.81016)] and [M. M. Wilde, A. Winter and D. Yang, “ Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy”, Preprint, arXiv:1306.1586].
For the entire collection see [Zbl 1329.68026].

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A17 Measures of information, entropy

Citations:

Zbl 1290.81016
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