Related papers: Platonic Bell inequalities for all dimensions
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…
Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum…
We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all…
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…
So far, various Bell type inequalities have been introduced to test the local realism in tripartite systems. In this article we consider a tripartite system with two measurements in each side and two outputs for each measurement. Then we…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…
The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we…
In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try…
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.…
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…
In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a…
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…
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 nonlocality is the resource that enables device-independent quantum information processing tasks. It is revealed through the violation of so-called Bell inequalities, indicating that the observed correlations cannot be reproduced by…
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…
The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say that a Bell inequality is normalized if its absolute value does not exceed 1 for any…
The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these…
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…
Extending previous results on a characterization of all equilateral triangle in space having vertices with integer coordinates ("in $\mathbb Z^3$"), we look at the problem of characterizing all regular polyhedra (Platonic Solids) with the…
Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson's bound, 2 \sqrt 2. However, for a given set of local observables, there are values in this range which no quantum state can attain. We…