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We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell…
On one side, so far a great part of the evidence accepted as proof of the alleged quantum non-locality relied on inhomogeneous Bell inequalities involving an additional assumption (no-enhancement) whose role had not been sufficiently…
Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum…
The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The…
Generalizations of Bell's theorem, particularly within quantum networks, are now being analyzed through the causal inference lens. However, the exploration of interventions, a central concept in causality theory, remains significantly…
Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities…
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source…
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…
Bell inequalities play a central role in certifying quantum correlations and underpin protocols such as device-independent quantum key distribution. However, enumerating all Bell inequalities for a given scenario remains intractable beyond…
Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators…
In this paper, we highlight how any Bell inequality for a configuration involving $n$ parties each performing one of $m$ binary-outcome measurements has a canonical form that is no-signalling-projection invariant. Specifically, the…
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local…
Determining whether an observed distribution of events generated in a quantum network is Bell local, i.e., if it admits an alternative realization in terms of independent local variables, is extremely challenging. Building upon…
We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible…
Bell inequalities can be studied both as constraints in the space of probability distributions and as expectation values of multipartite operators. The latter approach is particularly useful when considering outcomes as eigenvalues of…
We address the classical and quantum marginal problems, namely the question of simultaneous realizability through a common probability density in phase space of a given set of compatible probability distributions. We consider only…
The structure of Bell-type inequalities detecting genuine multipartite non-locality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original…
We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…
Bell inequalities are derived for any number of observers, any number of alternative setups for each one of them, and any number of distinct outcomes for each experiment. It is shown that if a physical system consists of several distant…
A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems,…