Related papers: Asymmetric quantum hypothesis testing with Gaussia…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…
In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper…
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can…
Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of…
We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…
The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the case when…
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szko{\l}a mapping. The lower bound provides a…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
We treat quantum counterparts of testing problems whose optimal tests are given by chi-square, t and F tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning quantum Gaussian states families, and…
We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…
In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a…
Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform…
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…