Classification of local realistic theories

TL;DR

This paper demonstrates that local realistic models effective in two-setting Bell experiments cannot be extended to three-setting experiments, highlighting limitations in their applicability across different measurement configurations.

Contribution

It introduces the novel result that two-setting local realistic models cannot replicate correlations in three-setting Bell experiments, unlike their success in two-setting scenarios.

Findings

Two-setting models fail for three-setting experiments.

Two-setting models cannot replicate three-measurement correlations.

Limitations of two-setting models in more complex measurement setups.

Abstract

Recently, it has shown that an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment (two-setting model), works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a {\it continuous-infinite} settings Bell experiment (infinite-setting model), even though there exist two-setting models for all directions in space. Hence, two-setting model does not have the property which infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in a {\it only discrete-three} settings Bell experiment (three-setting model), even though there exist two-setting models for the three measurement directions chosen in the given three-setting experiment. Hence, two-setting model does not have the property which three-setting model has.