Second-order asymptotics for quantum hypothesis testing
نویسندگان
چکیده
منابع مشابه
Second Order Asymptotics for Quantum Hypothesis Testing
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 h...
متن کاملA large-deviation type asymptotics in the quantum hypothesis testing
Recently, there has been a rise in the necessity for studies about the quantum hypothesis testing problem, related to the corresponding advance in the measuring technologies in quantum optics. This fundamental research subject in the quantum hypothesis testing problem was initiated by Helstrom [1] in the 1970s with a non-asymptotic study. Its asymptotic aspect has been studied by Hiai-Petz[2], ...
متن کاملFirst- and Second-Order Hypothesis Testing for Mixed Memoryless Sources
The firstand second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to ε, is called the ε-optimum exponent. In this paper, we first give the second-order ε-optimum exponent in the case where the null hypo...
متن کاملHYPOTHESIS TESTING FOR AN EXCHANGEABLE NORMAL DISTRIBUTION
Consider an exchangeable normal vector with parameters ????2, and ?. On the basis of a vector observation some tests about these parameters are found and their properties are discussed. A simulation study for these tests and a few nonparametric tests are presented. Some advantages and disadvantages of these tests are discussed and a few applications are given.
متن کاملSecond Order Asymptotics for Matrix Models
We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2014
ISSN: 0090-5364
DOI: 10.1214/13-aos1185