Related papers: On Composite Quantum Hypothesis Testing
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…
Given a sequence of random variables $X^n=X_1,\ldots, X_n$, discriminating between two hypotheses on the underlying probability distribution is a key task in statistics and information theory. Of interest here is the Stein exponent, i.e.…
Pairs of states, or "boxes" are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states. From this point of view,…
The generalized quantum Stein's lemma provides an explicit expression for the optimal error exponent when distinguishing many independent and identically distributed (iid) copies of a given bipartite state from the set of separable…
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…
We consider the task of distinguishing whether a quantum system is prepared in a state from one of several sets of quantum states. Assuming their convexity and stability under tensor product, we prove that the optimal error exponent for…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
The problem of testing two simple hypotheses in a general probability space is considered. For a fixed type-I error probability, the best exponential decay rate of the type-II error probability is investigated. In regular asymptotic cases…
We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is…
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…
The performance of quantum resource manipulation protocols, including key examples such as distillation of quantum entanglement, is measured in terms of the rate at which desired target states can be produced from a given noisy state.…
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…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
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…
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…
The hypothesis testing problem of two quantum states is treated. We show a new inequality between the error of the first kind and the second kind, which complements the result of Hiai and Petz to establish the quantum version of Stein's…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two…