Related papers: Platonic Bell inequalities for all dimensions
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Investigations of the boundary of the quantum correlation set through the derivation of quantum Bell inequalities have gained increased attention in recent years, which are related to Tsirelson's problem and have significant applications in…
We present a much simplified version of the CGLMP inequality for the 2 x 2 x d Bell scenario. Numerical maximization of the violation of this inequality over all states and measurements suggests that the optimal state is far from maximally…
It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a new derivation of the inequalities from non-trivial non-local theories and formulates a stronger Bell argument…
We report correlation measurements on two $^9$Be$^+$ ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution…
We define a property called nondegeneracy for Bell inequalities, which describes the situation that in a Bell setting, if a Bell inequality and involved local measurements are chosen and fixed, any quantum state with a given dimension and…
This paper focuses on the dynamics of the eight tridimensional principal slices of the tricomplex Mandelbrot set: the Tetrabrot, the Arrowheadbrot, the Mousebrot, the Turtlebrot, the Hourglassbrot, the Metabrot, the Airbrot (octahedron) and…
Quantum correlations are critical to our understanding of nature, with far-reaching technological and fundamental impact. These often manifest as violations of Bell's inequalities, bounds derived from the assumptions of locality and…
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair…
The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…
Non-classical quantum correlations underpin both the foundations of quantum mechanics and modern quantum technologies. Among them, Bell nonlocality is a central example. For bipartite Bell inequalities, nonlocal correlations obey strict…
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…
Regular polytopes, the generalization of the five Platonic solids in 3 space dimensions, exist in arbitrary dimension $n\geq-1$; now in {\rm dim}. 2, 3 and 4 there are \emph{extra} polytopes, while in general dimensions only the…
We experimentally demonstrate, using qubits encoded in photon polarization, that if two parties share a single reference direction and use locally orthogonal measurements they will always violate a Bell inequality, up to experimental…
Motivated by the relation between particle shape and packing, we measure the volume fraction $\phi$ occupied by the Platonic solids which are a class of polyhedron with congruent sides, vertices and dihedral angles. Tetrahedron, cube,…
In past work, the concept of connectors was introduced: directed tensors with the property that any contraction thereof defines a multipartite quantum Bell inequality, i.e., a linear restriction on measurement probabilities that holds in…
Multipartite nonlocality is of great fundamental interest and constitutes a useful resource for many quantum information protocols. However, demonstrating it in practice, by violating a Bell inequality, can be difficult. In particular,…
Euclidean volume ratios between quantum states with positive partial transpose and all quantum states in bipartite systems are investigated. These ratios allow a quantitative exploration of the typicality of entanglement and of its…
Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements…
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about…