Related papers: Statistical analysis of Bell tests via generalized…

Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…

We examine the satisfaction of Bell criteria for single realizations of quantum systems. This is possible via the joint noisy measurement of all observables involved in the Bell test.We readily find that every outcome violates Bell bounds…

Bell experiments can be used to generate private random numbers. An ideal Bell experiment would involve measuring a state of two maximally entangled qubits, but in practice any state produced is subject to noise. Here we consider how the…

Analysis of experimental data must sometimes deal with abrupt changes in the distribution of measured values. Setting upper limits on signals usually involves a veto procedure that excludes data not described by an assumed statistical…

Quantum theory is inconsistent with any local hidden variable model as was first shown by Bell. To test Bell inequalities two separated observers extract correlations from a common ensemble of identical systems. Since quantum theory does…

Separating signal from noise is central to experiments. Applying well-established statistical methods effectively to LLM evals requires consideration of their unique noise characteristics. We clearly define and measure three types of noise:…

Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private…

A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…

Derivation and experimental violation of Bell-like inequalities involve the measurement of in-compatible observables. Simple complementarity forbids the existence of such joint probabilitydistribution. Moreover, the measurement of…

Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and…

As the most important tool to provide high-level evidence-based medicine, researchers can statistically summarize and combine data from multiple studies by conducting meta-analysis. In meta-analysis, mean differences are frequently used…

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…

We present Bell tests for optical continuous variable systems, combining both hybrid measurements (i.e. measuring both particle and wave aspects of light) and heralded amplifiers. We discuss two types of schemes, in which the amplifier is…

Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments…

A key objective in conducting a Bell test is to quantify the statistical evidence against a local-hidden variable model (LHVM) given that we can collect only a finite number of trials in any experiment. The notion of statistical evidence is…

Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local…

Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…

We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main…

Consider a measurement in which the current coming out of a mesoscopic sample is filtered around a given frequency, amplified, measured and squared. Then this process is repeated many times and the results are averaged. Often, two such…