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Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational…
When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which…
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…
The I3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In case of the CHSH inequality the maximal quantum…
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…
Bell inequalities are an important tool for studying non-locality, however quickly become computationally intractable as the system size grows. We consider a novel method for finding an upper bound for the quantum violation of such…
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…
A systematic approach is presented to construct non-homogeneous two- and three-qubit Bell-type inequalities. When projector-like terms are subtracted from homogeneous two-qubit CHSH polynomial, non-homogeneous inequalities are attained and…
We show that it is possible to find maximal violations of the CHSH-Bell inequality using only position measurements on a pair of entangled non-relativistic free particles. The device settings required in the CHSH inequality are done by…
Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced…
We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. The tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities…
Given a sequence of pairs of spin-one half particles in the singlet state, assume that Alice measures the normalized projections along some vector of the spins of one vector per pair along that vector while Bob measures the normalized…
Many typical Bell experiments can be described as follows. A source repeatedly distributes particles among two spacelike separated observers. Each of them makes a measurement, using an observable randomly chosen out of several possible…
Bell correlation inequalities for two sites and 2+n or 3+3 two-way measurements ("dichotomic observables") are considered. In the 2+n case, any facet of the classical experience polytope is defined by a CHSH inequality involving only two…
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.…
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…
In this paper, we highlight how any Bell inequality for a configuration involving $n$ parties each performing one of $m$ binary-outcome measurements has a canonical form that is no-signalling-projection invariant. Specifically, the…
We study a class of Bell inequalities and find their maximum quantum violation. These inequalities involve n parties, two measurements per party, with each measurement having two outcomes. The n=2 case corresponds to the CH inequality. We…
The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The…
We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular we describe several Bell inequalities which appear to be optimal with respect to…