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Seen from the modern lens of causal inference, Bell's theorem is nothing else than the proof that a specific classical causal model cannot explain quantum correlations. It is thus natural to move beyond Bell's paradigmatic scenario and…

Bell's theorem prompts us with a fundamental inquiry: what is the simplest scenario leading to the incompatibility between quantum correlations and the classical theory of causality? Here we demonstrate that quantum non-classicality is…

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…

Bell's theorem, a cornerstone of quantum theory, shows that quantum correlations are incompatible with a classical theory of cause and effect. Through the lens of causal inference, it can be understood as a particular case of causal…

Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…

Since Bell's theorem, it is known that the concept of local realism fails to explain quantum phenomena. Indeed, the violation of a Bell inequality has become a synonym of the incompatibility of quantum theory with our classical notion of…

Explaining observations in terms of causes and effects is central to all of empirical science. Correlations between entangled quantum particles, however, seem to defy such an explanation. To recover a causal picture in this case, some of…

From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization…

Classical and quantum physics impose different constraints on the joint probability distributions of observed variables in a causal structure. These differences mean that certain correlations can be certified as non-classical, which has…

Causal networks beyond that in the paradigmatic Bell's theorem can lead to new kinds and applications of non-classical behavior. Their study, however, has been hindered by the fact that they define a non-convex set of correlations and only…

Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography…

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…

Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers…

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…

The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…

We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with $N$ observers, each of which performs one out of two possible three-outcome…

Quantum measurements are crucial for quantum technologies and give rise to some of the most classically counter-intuitive quantum phenomena. As such, the ability to certify the presence of genuinely non-classical joint measurements in a…

Bell inequalities follow from a set of seemingly natural assumptions about how to provide a causal model of a Bell experiment. In the face of their violation, two types of causal models that modify some of these assumptions have been…

The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We…

It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection…