Open AccessEffects of white noise on the violation of Bell-type inequalities based on probability theory
Author(s) -
Arijit Dutta,
Jaewan Kim,
Jinhyoung Lee
Publication year - 2021
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/ac0085
Subject(s) - physics , observable , inequality , infinitesimal , type (biology) , white noise , statistical physics , bell test experiments , quantum , bell's theorem , theoretical physics , pure mathematics , mathematical physics , quantum mechanics , statistics , quantum entanglement , mathematical analysis , mathematics , ecology , biology
We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility v c .