Related papers: Bell inequalities for three particles
We develop a systematic approach to establish Bell inequalities for qubits based on the Cauchy-Schwarz inequality. We also use the concept of distinct "roots" of Bell function to classify some well-known Bell inequalities for qubits. As…
A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable…
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…
We present a method to derive explicit forms of tight correlation function Bell inequalities for three systems and dichotomic observables, which involve three settings for each observer. We also give sufficient conditions for quantum…
We present a set of Bell inequalities for multiqubit quantum systems. These Bell inequalities are shown to be able to detect multiqubit entanglement better than previous Bell inequalities such as Werner-Wolf-Zukowski- Brukner ones.…
We computationally investigate the complete polytope of Bell inequalities for 2 particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection of this problem to the computationally hard…
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…
We present an analysis of the structure of Bell inequalities, mainly for the case of N qubits with two observables each. We show that these inequalities are related to Hadamard matrices and define Bell polynomials (in one variable) as an…
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 discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of…
We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased…
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…
For two particles with different spin, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and 1/2; spin-1/2 and 3/2. We show that for these states Bell's inequality is violated.
Multipartite Bell-type inequalities are derived for general systems. They involve up to eight observables with arbitrary spectra on each site. These inequalities are closely related to the algebras of quaternions and octonions.
Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared.…
We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and…
We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local realistic theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems 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…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
A derivation method is given which leads to a series of tight Bell inequalities for experiments involving N parties, with binary observables, and three possible local settings. The approach can be generalized to more settings. Ramifications…