Related papers: Statistical analysis on testing of an entangled st…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…
We show, by explicit examples, that the Jaynes inference scheme based on maximization of entropy can produce inseparable states even if there exists a separable state compatible with the measured data. It can lead to problems with…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We propose a scheme for the generation of entangled states for two atoms trapped in separate cavities coupled to each other. The scheme is based on the competition between the unitary dynamics induced by the classical fields and the…
We address the witnessing of quantum correlations beyond the limits imposed by an ensemble statistical average. By relying upon the continuous observation of a single quantum open system under the action of classical or quantum noise, we…
The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium…
Based on correlations of coherently displaced photon-numbers, we derive entanglement criteria for the purpose to verify non-Gaussian entanglement. Our construction method enables us to verify bipartite and multipartite entanglement of…
We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice…
Lately, much interest has been directed towards designing setups that achieve decisive tests of local realism. Here we present Bell tests with measurements based on linear optical displacements and single-photon detection. The scheme…
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…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the…
We present a method to quantify entanglement in mixed states of highly symmetric systems. Symmetry constrains interactions between parts and predicts the degeneracies of the states. While symmetry alone produces entangled eigenstates, the…
We report an experimental demonstration of effective entanglement in a prepare&measure type of quantum key distribution protocol. Coherent polarization states and heterodyne measurement to characterize the transmitted quantum states are…
We apply a distance-based Bell-test analysis method [E. Knill et al., Phys. Rev. A. 91, 032105 (2015)] to three experimental data sets where conventional analyses failed or required additional assumptions. The first is produced from a new…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…
Recently a likelihood-based methodology has been developed by the Collaboratory for the Study of Earthquake Predictability (CSEP) with a view to testing and ranking seismicity models. We analyze this approach from the standpoint of possible…