Effects of white noise on Bell theorem for qudits

TL;DR

This paper develops new Bell-type inequalities for high-dimensional quantum systems using statistical quasi-separations, revealing conditions under which quantum mechanics violates these inequalities with minimal noise.

Contribution

It introduces two types of statistical quasi-separations to construct Bell inequalities for arbitrary dimensions and measurement settings, expanding the theoretical framework for quantum nonlocality.

Findings

Derived Bell inequalities for qudits with multiple measurement settings

Identified conditions for quantum violations with infinitesimal critical visibility

Extended Bell inequality construction using triangle inequalities

Abstract

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 $v_c$.