Related papers: Dimension-Independent Bounds for Hardy's Experimen…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…
Nonlocality can be studied through different approaches, such as Bell's inequalities, and it can be found in numerous quantum states, including GHZ states or graph states. Hardy's paradox, or Hardy-type nonlocality, provides a way to…
This work aims at exploring whether the nonlocal correlations due to quantum entanglement could exist without nonlocal causation. This is done with the aid of a toy model to investigate whether the ability of two quantum entangled particles…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Bell's inequality fundamentally changed our understanding of quantum mechanics. Bell's insight that non-local correlations between quantum systems cannot be explained classically can be verified experimentally, and has numerous applications…
In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of "quantum theory from five reasonable axioms." Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not…
Device independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a "black box" scenario where only correlations between preparations, measurements and outcomes are considered. We address…
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…
Let $X_1,\ldots,X_N$, $N>n$, be independent random points in $\mathbb{R}^n$, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more…
We present a simple gedanken experiment in which a compact object traverses a spacetime with three macroscopic spatial dimensions and $n$ compact dimensions. The compactification radius is allowed to vary, as a function of the object's…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
Bell showed 50 years ago that quantum theory is nonlocal via his celebrated inequalities, turning the issue of quantum nonlocality from a matter of taste into a matter of test. Years later, Hardy proposed a test for nonlocality without…
Multipartite quantum states may exhibit different types of quantum entanglement in that they cannot be converted into each other by local quantum operations only, and fully understanding mathematical structures of different types of…
We have studied the possibility of post-quantum theories more nonlocal than the (standard) quantum theory using the modification of the quantum probability rule under the no-signaling condition. For this purpose we have considered the…
Quantum paradoxes show that quantum statistics can exceed the limits of positive joint probabilities for physical properties that cannot be measured jointly. It is therefore impossible to describe the relations between the different…
The $E_8 \otimes E_8$ octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum…
Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood…
Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways.…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical…