Related papers: (Nearly) optimal P-values for all Bell inequalitie…
We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell's S or Eberhard's J. Further…
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,…
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be…
In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a p-value it will give for a physical experiment. Here we show that to obtain a small expected p-value it is…
This chapter demystifies P-values, hypothesis tests and significance tests, and introduces the concepts of local evidence and global error rates. The local evidence is embodied in \textit{this} data and concerns the hypotheses of interest…
An alternative method of detection-loophole-free Bell test is proposed using local hidden variable (LHV) models with optimal detection efficiencies. A framework for constructing such optimal LHV models is presented. Optimal LHV models for…
In science, the most widespread statistical quantities are perhaps $p$-values. A typical advice is to reject the null hypothesis $H_0$ if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding…
Bell's theorem shows that no hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this work we demonstrate that by…
Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. In this paper we show that all experiments that aim to prove Bell's theorem do not actually achieve…
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…
The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, usually the CHSH inequality. However, the…
On one side, so far a great part of the evidence accepted as proof of the alleged quantum non-locality relied on inhomogeneous Bell inequalities involving an additional assumption (no-enhancement) whose role had not been sufficiently…
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue…
Bell inequalities play a central role in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer…
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…
The problem of computing the local hidden variable (LHV) value of a Bell inequality plays a central role in the study of quantum nonlocality. In particular, this problem is the first step towards characterizing the LHV polytope of a given…
Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the…
The no-signalling principle is a fundamental assumption in Bell-inequality and quantum-steering experiments. Nonetheless, experimental imperfections can lead to apparent violations beyond those expected from finite-sample statistics. Here,…
Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…