Related papers: Optimal statistical analyses of Bell experiments

We experimentally demonstrate, using qubits encoded in photon polarization, that if two parties share a single reference direction and use locally orthogonal measurements they will always violate a Bell inequality, up to experimental…

The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682-686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on…

We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the…

In this Letter, we explore the possibility of developing Bell inequalities predicated on models using a single Local Hidden Variable (s-LHV), a strict subset of general LHV models. Because of the less strenuous constraints imposed by s-LHV…

We analyse the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical) statistical correction…

Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of…

Likelihood ratio tests and the Wilks theorems have been pivotal in statistics but have rarely been explored in network models with an increasing dimension. We are concerned here with likelihood ratio tests in the $\beta$-model for…

Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…

The observation that violating Bell inequalities with high probability is possible even when the local measurements are randomly chosen, as occurs when local measurements cannot be suitably calibrated or the parties do not share a common…

The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like…

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…

Another Bell test "loophole" - imperfect rotational invariance - is explored, and novel realist ideas on parametric down-conversion as used in recent "quantum entanglement" experiments are presented. The usual quantum theory of entangled…

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…

Bell nonlocality between distant quantum systems---i.e., joint correlations which violate a Bell inequality---can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to…

We propose a practical scheme to use photons from causally disconnected cosmic sources to set the detectors in an experimental test of Bell's inequality. In current experiments, with settings determined by quantum random number generators,…

A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory…

We study a statistical framework for replicability based on a recently proposed quantitative measure of replication success, the sceptical $p$-value. A recalibration is proposed to obtain exact overall Type-I error control if the effect is…

Bell inequalities rest on three fundamental assumptions: realism, locality, and free choice, which lead to nontrivial constraints on correlations in very simple experiments. If we retain realism, then violation of the inequalities implies…