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We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the measure satisfies a transport-entropy inequality. We extend some…

Probability · Mathematics 2011-05-27 Emmanuel Boissard

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

Statistics Theory · Mathematics 2025-02-24 Huiming Zhang , Song Xi Chen

Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to…

Methodology · Statistics 2021-10-22 Steven G. Xu , Brian J. Reich

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these…

This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…

Econometrics · Economics 2018-04-12 Hiroaki Kaido , Jiaxuan Li , Marc Rysman

We prove new concentration inequalities for quantum spin systems which apply to any local observable measured on any product state or on any state with exponentially decaying correlations. Our results do not require the spins to be arranged…

Mathematical Physics · Physics 2025-06-17 Giacomo De Palma , Davide Pastorello

Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…

Physics Education · Physics 2016-02-22 Chandralekha Singh , Guangtian Zhu

The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…

Quantum Physics · Physics 2016-05-16 Gregory A. Howland , James Schneeloch , Daniel J. Lum , John C. Howell

Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…

Quantum Physics · Physics 2024-01-18 Qing Ai , Yang-Yang Wang , Jing Qiu

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical…

Quantum Physics · Physics 2017-10-26 Christian de Ronde

The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in…

Statistics Theory · Mathematics 2025-04-23 Alicja Jokiel-Rokita , Sylwester Piątek , Rafał Topolnicki

The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…

Quantum Physics · Physics 2014-07-01 Holger F. Hofmann

Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…

Mathematical Physics · Physics 2009-10-29 Henning Bostelmann , Christopher J. Fewster

We propose an approach to measuring nonresonant coupled systems, which gives a parametrically smaller error than the conventional fast projective measurements. The approach takes into account that, due to the coupling, excitations are not…

Quantum Physics · Physics 2009-03-05 L. Fedichkin , M. Shapiro , M. I. Dykman

Knowledge of optimal quantum measurements is important for a wide range of situations, including quantum communication and quantum metrology. Quantum measurements are usually optimised with an ideal experimental realisation in mind. Real…

Quantum Physics · Physics 2015-06-03 Erika Andersson

In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…

Statistical Mechanics · Physics 2020-09-08 Gyula I. Toth

Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…

Quantum Physics · Physics 2009-08-25 Matteo G. A. Paris

We show that there exist informationally incomplete phase space observables such that the Cartesian margins are informationally equivalent with position and momentum. This shows that it is possible to reconstruct the position and momentum…

Quantum Physics · Physics 2015-06-04 Jussi Schultz

We use Pesin theory to study possible equilibrium measures for piecewise monotone maps of the interval. The maps may have unbounded derivative.

Dynamical Systems · Mathematics 2019-02-14 Neil Dobbs

Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer…

Methodology · Statistics 2016-03-21 Jakob Runge