Related papers: Significance tests and sample homogeneity loophole
This paper considers the problem of testing temporal homogeneity of $p$-dimensional population mean vectors from the repeated measurements of $n$ subjects over $T$ times. To cope with the challenges brought by high-dimensional longitudinal…
The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et. al. showed how to make this statement quantitative, using semidefinite programming to…
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair…
At first sight, the use of an everywhere positive Wigner function as a probability density to perform stochastic simulations in quantum optics seems equivalent to the introduction of local hidden variables, thus preventing any violation of…
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the…
We show that homodyne measurements can be used to demonstrate violations of Bell's inequality with Gaussian states, when the local rotations used for these types of tests are implemented using nonlinear unitary operations. We reveal that…
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical…
Objections to the use of inequalities to address foundational issues are considered and shown to be invalid. The Clauser-Horne (CH) inequality is considered and interpreted in this light. It is shown that, applied correctly, the CH…
Bell inequalities are a cornerstone of quantum physics. By carefully selecting measurement bases (typically polarization), their violation certifies quantum entanglement. Such measurements are disrupted by the presence of optical disorder…
We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic non-maximally entangled two-qubit state and two alternative measurement…
Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson…
Superselection rules (SSRs) constrain the allowed states and operations in quantum theory. They limit preparations and measurements hence impact upon our ability to observe non-locality, in particular the violation of Bell inequalities. We…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
Equivalence testing is of emerging importance in genomics studies but has hitherto been little studied in this content. In this paper, we define the notion of equivalence of gene expression and determine a `strength of evidence' measure for…
One of the most notable aspects of quantum systems is that their components can exhibit correlations much stronger than those allowed by classical physics. Two examples of quantum correlations are quantum entanglement and Bell nonlocality,…
Loophole-free Bell tests for quantum nonlocality and long-distance secure communication require photodetection efficiencies beyond a threshold eta_{crit} that depends on the Bell inequality and the noise affecting the entangled state…
The customary use of P-values in scientific research has been attacked as being ill-conceived, and the utility of P-values has been derided. This paper reviews common misconceptions about P-values and their alleged deficits as indices of…
The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and…
Since its debut in the 18th century, the P-value has been an important part of hypothesis testing-based scientific discoveries. As the statistical engine accelerates, questions are beginning to be raised, asking to what extent scientific…
We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an…