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Quantum contextuality is a nonintuitive property of quantum mechanics, that distinguishes it from any classical theory. A complementary quantum property is quantum nonlocality, which is an essential resource for many quantum information…
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…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for…
A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
We consider four measures of contextuality, chosen for being based on the fundamental properties of the notion of contextuality, and for being applicable to arbitrary systems of measurements, both without and with disturbance. We have…
The sheaf theoretic description of non-locality and contextuality by Abramsky and Brandenburger sets the ground for a topological study of these peculiar features of quantum mechanics. This viewpoint has been recently developed thanks to…
We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon…
Quantum information processing shows advantages in many tasks, including quantum communication and computation, comparing to its classical counterpart. The essence of quantum processing lies on the fundamental difference between classical…
A new quantum ontology of quantum mechanics has been proposed recently. This ontology is based on impossible to realize measurements which need to be performed repeatedly on the same single physical system or on the same pair of physical…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…
According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the…
In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is…
It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…
The title refers to the Free Will Theorem by Conway and Kochen whose flashy formulation is: if experimenters possess free will, then so do particles. In more modest terms, the theorem says that individual pairs of spacelike separated…
Quantum contextuality in systems of identical bosonic particles is explicitly exhibited via the maximum violation of a suitable inequality of Clauser-Horne-Shimony-Holt type. Unlike the approaches considered so far, which make use of…