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Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact,…
We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes, and use it to give a simple proof that the maximally entangled state of two d dimensional quantum systems has no local component. That…
Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements,…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
In a recent article [Phys. Rev. A 54, 1793 (1996)] Krenn and Zeilinger investigated the conditional two-particle correlations for the subensemble of data obtained by selecting the results of the spin measurements by two observers 1 and 2…
For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality [Loubenets, J. Math. Phys. 53, 022201 (2012)]. In the present article, for the maximal violation of Bell inequalities…
We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a…
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…
It is by now well-established that there exist non-local games for which the best entanglement-assisted performance is not better than the best classical performance. Here we show in contrast that any two-player XOR game, for which the…
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…
All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a…
In this paper we introduce a simple and natural bipartite Bell scenario, by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell…
Imagine two parties, Alice and Bob who share an entangled quantum state. A well-established result that if Alice performs two-outcome measurement on the portion of the state in her possession and Bob does likewise, they are able to produce…
Two important ingredients necessary for obtaining Bell nonlocal correlations between two spatially separated parties are an entangled state shared between them and an incompatible set of measurements employed by each of them. We focus on…
We have determined numerically the maximum quantum violation of over 100 tight bipartite Bell inequalities with two-outcome measurements by each party on systems of up to four dimensional Hilbert spaces. We have found several cases,…
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…
It is well known that the maximal violation of the Bell's inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an $n$-qubit state has not been…
Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled…
Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication…