Convexity properties of the quantum Rényi divergences, with applications to the quantum Stein's lemma
arXiv:1407.1067
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 Rényi divergence, recently introduced in [Müller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013)], and [Wilde, Winter, Yang, arXiv:1306.1586].
TQC 2014 conference paper based on arXiv:1310.7525. The main result, Theorem 9, is new