Geometric chained inequalities for higher-dimensional systems

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.

7 pages, Almost identical with the published version

References in corpus (8)

• Bell nonlocality
• Multi-photon entanglement and interferometry
• No extension of quantum theory can have improved predictive power
• Maximally Non-Local and Monogamous Quantum Correlations
• Logical Bell Inequalities
• Hidden variable models for quantum theory cannot have any local part
• Two-photon Franson-type experiments and local realism
• Ladder proof of nonlocality without inequalities and without probabilities

Cited by in corpus (5)

• Two Copies of the Einstein-Podolsky-Rosen State of Light Lead to Refutation of EPR Ideas
• Maximal Non-Classicality in Multi-Setting Bell Inequalities
• Geometric extension of Clauser-Horne inequality to more qubits
• Why quantum correlations are shocking
• Genuine monogamy relations in no-signaling theories - a geometric approach