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Bell non-locality is a fundamental feature of quantum mechanics whereby measurements performed on "spatially separated" quantum systems can exhibit correlations that cannot be understood as revealing predetermined values. This is a special…
Quantum correlations that violate the Bell inequality cannot be explained by any (measurement independent) local hidden variable theory. However, the violation only implies incompatibility of the underlying assumptions of reality, locality,…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
Bell's Theorem from 1964 and the (Strong) Free Will Theorem of Conway and Kochen from 2009 both exclude deterministic hidden variable theories (or, in modern parlance, `ontological models') that are compatible with some small fragment of…
Contextuality, a key resource for quantum advantage, describes systems in which the outcome of a measurement is not independent of other compatible measurements, in contrast to classical hidden-variable descriptions. We investigate the…
This paper presents a topological learning-theoretic perspective on causal inference by introducing a series of topologies defined on general spaces of structural causal models (SCMs). As an illustration of the framework we prove a…
A major challenge in estimating treatment effects in observational studies is the reliance on untestable conditions such as the assumption of no unmeasured confounding. In this work, we propose an algorithm that can falsify the assumption…
It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a new derivation of the inequalities from non-trivial non-local theories and formulates a stronger Bell argument…
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…
We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via nonnegative values of real-valued…
Experiments motivated by Bell's theorem have led some physicists to conclude that quantum theory is nonlocal. However, the theoretical basis for such claims is usually taken to be Bell's Theorem, which shows only that if certain predictions…
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Device-independent certifications employ Bell tests to guarantee the proper functioning of an apparatus from the sole knowledge of observed measurement statistics, i.e. without assumptions on the internal functioning of the devices. When…
It is shown that it is possible to rule out all local and stochastic hidden variable models accounting for the quantum mechanical predictions implied by almost any entangled quantum state vector of any number of particles whose Hilbert…
Bell nonlocality is an intriguing property of quantum mechanics with far reaching consequences for information processing, philosophy and our fundamental understanding of nature. However, nonlocality is a statement about static correlations…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…