Related papers: Quantum hypothesis testing with group symmetry
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…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
We investigate the ability of a quantum measurement device to discriminate two states or, generically, two hypothesis. In full generality, the measurement can be performed a number $n$ of times, and arbitrary pre-processing of the states…
In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In…
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…
In this paper, we treat an asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state and the completely mixed state by one-way LOCC, two-way LOCC, and…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
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 Stein's Lemma is a cornerstone of quantum statistics and concerns the problem of correctly identifying a quantum state, given the knowledge that it is one of two specific states ($\rho$ or $\sigma$). It was originally derived in the…
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…
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…
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…
We address the one-dimensional quantum Ising model as an example of system exhibiting criticality and study in some details the discrimination problem for pairs of states corresponding to different values of the coupling constant. We…
We consider decision problems on finite sets of hypotheses represented by pairwise different shift-invariant states on a quantum spin chain. The decision in favor of one of the hypotheses is based on outputs of generalized measurements…
The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing…
We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…
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…