Related papers: Significance tests and sample homogeneity loophole
This paper investigates type I error violations that occur when blinded sample size reviews are applied in equivalence testing. We give a derivation which explains why such violations are more pronounced in equivalence testing than in the…
Statistical significance testing is used in natural language processing (NLP) to determine whether the results of a study or experiment are likely to be due to chance or if they reflect a genuine relationship. A key step in significance…
There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general…
It has long been known that the "detection loophole", present when detector efficiencies are below a critical figure, could open the way for alternative "local realist" explanations for the violation of Bell tests. It has in recent years…
Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples. To study these tests in small samples, we consider the likelihood ratio test and define an accurate index,…
We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number…
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…
In the analysis of experiments designed to reveal violation of Bell-type inequalities, it is usually assumed that any hidden variables associated with the nth particle pair would be independent of measurement choices and outcomes for the…
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…
Null hypothesis significance tests and p values are widely used despite very strong arguments against their use in many contexts. Confidence intervals are often recommended as an alternative, but these do not achieve the objective of…
For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
P-hacking is prevalent in reality but absent from classical hypothesis testing theory. As a consequence, significant results are much more common than they are supposed to be when the null hypothesis is in fact true. In this paper, we build…
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 address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $\eta$ that must be surpassed to avoid the…
We discuss Bell nonlocality in quantum networks with unreliable sources. Our main result is a condition on the observed data which ensures that inconclusive events can be safely discarded, without introducing any loophole. More formally, we…
A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of $\sqrt 2$,…
In single-particle entanglement (SPE) two degrees of freedom of a single particle are entangled. SPE is a resource that can be exploited both in quantum communication protocols and in experimental tests of noncontextuality based on the…
Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multi-outcome measurements is often only emulated via a…
Randomization tests deliver exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. In practice, achieving these guarantees often requires stronger conditions than the null hypothesis of primary…