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Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum…
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,…
Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making…
Entanglement, one of the most intriguing aspects of quantum mechanics, marks itself into different features of quantum states. For this reason different criteria can be used for verifying entanglement. In this paper we review some of the…
Bell non-locality represents one of the most striking departures of quantum mechanics from classical physics. It shows that correlations between space-like separated systems allowed by quantum mechanics are stronger than those present in…
Bell's theorem was a cornerstone for our understanding of quantum theory, and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been…
Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence…
Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical…
Besides using the laser beam, it is very tempting to directly testify the Bell inequality at high energy experiments where the spin correlation is exactly what the original Bell inequality investigates. In this work, we follow the proposal…
A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…
For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all…
Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands…
While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to…
In quantum information, lifting is a systematic procedure that can be used to derive---when provided with a seed Bell inequality---other Bell inequalities applicable in more complicated Bell scenarios. It is known that the procedure of…
Violation of Bell inequalities in bipartite systems represented by mutually-commuting von Neumann algebras has pioneered the study of vacuum entanglement in algebraic quantum field theory. It is unexpected that the maximal violation of Bell…
In the literature on $K$-locality ($K\geq2$) networks, the local hidden variables are strictly distributed in the specific observers rather than the whole ones. Regarding genuine Bell locality, all local hidden variables, as classical…
The EPR paradox is known as an interpretive problem, as well as a technical discovery in quantum mechanics. It defined the basic features of two-quantum entanglement, as needed to study the relationships between two non-commuting variables.…
Violations of a Bell inequality are reported for an experiment where one of two entangled qubits is stored in a collective atomic memory for a user-defined time delay. The atomic qubit is found to preserve the violation of a Bell inequality…
Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell…
Bell's theorem is a no-go theorem stating that quantum mechanics cannot be reproduced by a physical theory based on realism, freedom to choose experimental settings and two locality conditions: setting (SI) and outcome (OI) independence. We…