Related papers: Quaternions, octonions and Bell-type inequalities
We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define…
We present a set of Bell inequalities that gives rise to a finer classification of the entanglement for tripartite systems. These inequalities distinguish three possible bi-separable entanglements for three-qubit states. The three Bell…
Relatively few families of Bell inequalities have previously been identified. Some examples are the trivial, CHSH, I_{mm22}, and CGLMP inequalities. This paper presents a large number of new families of tight Bell inequalities for the case…
Bell inequalities for position measurements are derived using the bits of the binary expansion of position-measurement results. Violations of these inequalities are obtained from the output state of the Non-degenerate Optical Parametric…
We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum…
We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are…
The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical…
Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate…
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 provide an overview of the connections between Bell's inequalities and algebraic structure.
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from…
We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e. that the N-particle system is composed of subsystems which may be correlated in any way (e.g. entangled) but which are uncorrelated with respect…
We establish a relation between the two-party Bell inequalities for two-valued measurements and a high-dimensional convex polytope called the cut polytope in polyhedral combinatorics. Using this relation, we propose a method, triangular…
The recently proposed (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91 (2015), 052110) group theoretical approach to the problem of breaking the Bell inequalities is applied to $S_4$ group. The Bell inequalities based on the choice of…
We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable $n$-particle density operators on an arbitrary dimensional space. This methodology enables us to truly derive a tight quadratic inequality as tests for…
A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A…
Which nonlocal correlations can be obtained, when a party has access to more than one subsystem? While traditionally nonlocality deals with spacelike separated parties, this question becomes important with quantum technologies that connect…
We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the…
Finding all Bell inequalities for a given number of parties, measurement settings, and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can…
Bell inequalities are a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models…