1208.1400 (Ke Li)
Ke Li
In the asymptotic theory of quantum hypothesis testing, the error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states, in an increasing way. This is well known as the direct part and strong converse of quantum Stein's lemma. Here we look into the behavior of this sudden change and have make it clear how the error of first kind grows according to a lower order of the error exponent of the second kind, and hence, we obtain the second order asymptotics for quantum hypothesis testing. Our method is elementary, based on basic linear algebra and probability theory. It deals with the achievability part and the converse part in a unified framework, with a clear geometric picture.
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http://arxiv.org/abs/1208.1400
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