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One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations…
To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average…
The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in Quantum theory is an intriguing one in this…
Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices and therefore provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for…
Recently Bell-type inequalities were introduced in Phys. Rev. A \textbf{85}, 032119 (2012) to analyze the correlations emerging in an entanglement swapping scenario characterized by independence of the two sources shared between three…
The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can in principle be revealed by measurements.…
Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such protocols typically specify the types of communication allowed, and the degrees of trust required, between the referee and each…
We describe a strictly classical dice game, which emulates the main features of the EPR experiment, including violation of Bell's inequalities. Therefore, the standard interpretation that Bell's theorem provides necessary conditions for…
A Bell test is a randomized trial that compares experimental observations against the philosophical worldview of local realism. A Bell test requires spatially distributed entanglement, fast and high-efficiency detection and unpredictable…
Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory - nonlocality. Despite the…
Violation of Bell inequality (or, Bell-type inequalities) by nonlocal correlations is justified by relaxation of at least one of the plausible physical constraints used to model such inequality. Based on this fact, in this letter we present…
Nonlocal game as a novel witness of the nonlocality of entanglement is of fundamental importance in various fields. The known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks of single entanglement.…
We present a tight inequality to test the dynamical nature of spacetime. A general-relativistic violation of that inequality certifies change of curvature, in the same sense as a quantum-mechanical violation of a Bell inequality certifies a…
Recently Wang et al. have reported a violation of a Bell inequality without entanglement [arXiv:2507.07756]. We show that their result is an artifact of postselection. It is well known that postselection may yield Bell inequality…
What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties…
We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…
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…
Bell's theorem implies that the outcomes of local measurements on two maximally entangled systems cannot be simulated without classical communication between the parties. The communication cost is finite for n Bell states, but it grows…
A bipartite perfect quantum strategy (BPQS) allows two players who cannot communicate with each other to always win a nonlocal game. BPQSs are rare but fundamental in light of some recent results in quantum information, computation, and…