Richard

https://arxiv.org/abs/2001.07507

Incompleteness in the Bell Theorem Using Non-contextual Local Realistic Model

Koji Nagata, Tadao Nakamura & Han Geurdes

International Journal of Theoretical Physics

ISSN 0020-7748 Volume 59 Number 2

Int J Theor Phys (2020) 59:313-320 DOI 10.1007/s10773-019-04312-3

https://link.springer.com/article/10.1007/s10773-019-04312-3

Here, we consider the Bell experiment for a system described by multipartite states in the case where n-dichotomic observables are measured per site. If n is two, we consider a two-setting Bell experiment. If n is three, we consider a three-setting Bell experiment. Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment. Three-setting model is an explicit local realistic model for the values of a correlation function, given in a three-setting Bell experiment. In the non-contextual scenario, there is not the difference between three-setting model and two-setting model. And we cannot classify local realistic theories in this case. This says that we can construct three-setting model from two-setting model. Surprisingly we can discuss incompleteness in the Bell theorem using non-contextual model. On the other hand, in the contextual scenario, there is the difference between three-setting model and two-setting model. This says that we must distinguish three-setting model from two-setting model. And we can classify local realistic theories in this case.