Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order asymptotics for quantum hypothesis testing   In the asymptotic theory of quantum hypothesis testing, the minimal 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
smoothly 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. This actually implies quantum Stein's lemma as a special case.
Meanwhile, our analysis also yields tight bounds for the case of finite sample
size. These results have potential applications in quantum information theory.
Our method is elementary, based on basic linear algebra and probability theory.
It deals with the achievability part and the optimality part in a unified
fashion.

4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org