Related papers: Looking for symmetric Bell inequalities
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…
Full-correlation Bell-like inequalities represent an important subclass of Bell-like inequalities that have found applications in both a better understanding of fundamental physics and in quantum information science. Loosely speaking, these…
Bell inequalities play a central role in certifying quantum correlations and underpin protocols such as device-independent quantum key distribution. However, enumerating all Bell inequalities for a given scenario remains intractable beyond…
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…
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…
The correlations that admit a local hidden-variable model are described by a family of polytopes, whose facets are the Bell inequalities. The CHSH inequality is the simplest such Bell inequality and is a facet of every Bell polytope. We…
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…
Characterizing the set of all Bell inequalities is a notably hard task. An insightful method of solving it in case of Bell correlation inequalities for scenarios with two dichotomic measurements per site - for arbitrary number of parties -…
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings or measurement outcomes. In this article, such "liftings" of Bell inequalities are…
Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on…
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…
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…
We present a prescription for obtaining Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give examples of some families of such inequalities. The inequalities are violated by certain classes…
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…
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…
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…
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…
Facet inequalities play an important role in detecting the nonlocality of a quantum state. The number of such inequalities depends on the Bell test scenario. With the increase in the number of parties, measurement outcomes, or/and the…
We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We develop a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult.…
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…