Geometric chained inequalities for higher-dimensional systems

TL;DR

This paper develops geometric chained Bell inequalities for systems of any dimension, demonstrating contradictions with quantum mechanics and local realism, and extending Bell's theorem to near-perfect correlations.

Contribution

It introduces a comprehensive theory of geometric chained Bell inequalities applicable to higher-dimensional systems, expanding the scope of Bell's theorem.

Findings

Maximally entangled states violate the inequalities, leading to contradictions with local realism.

The inequalities can be used to formulate Bell's theorem with correlations close to perfect.

Contradictions hold for systems of any dimension.

Abstract

For systems of an arbitrary dimension, a theory of geometric chained Bell inequalities is presented. The approach is based on chained inequalities derived by Pykacz and Santos. For maximally entangled states the inequalities lead to a complete $0=1$ contradiction with quantum predictions. Local realism suggests that the probability for the two observes to have identical results is $1$ (that is a perfect correlation is predicted), whereas quantum formalism gives an opposite prediction: the local results always differ. This is so for any dimension. We also show that with the inequalities, one can have a version of Bell's theorem which involves only correlations arbitrarily close to perfect ones.