Higher-Dimensional Bell Inequalities with Noisy Qudits

TL;DR

This paper investigates how the violation of higher-dimensional Bell inequalities, specifically the Collins-Gisin-Linden-Massar-Popescu inequality, is affected by realistic noise sources in qudits, revealing decreased robustness with increasing dimension.

Contribution

It provides a detailed analysis of noise effects on Bell inequality violations in qudits, challenging the assumption of increased robustness at higher dimensions.

Findings

Robustness to noise decreases as qudit dimension increases.

Analysis based on realistic noise models relevant to superconducting resonator qudits.

Results suggest limitations for high-dimensional Bell tests under noisy conditions.

Abstract

Generalizations of the classic Bell inequality to higher dimensional quantum systems known as qudits are reputed to exhibit a higher degree of robustness to noise, but such claims are based on one particular noise model. We analyze the violation of the Collins-Gisin-Linden-Massar-Popescu inequality subject to more realistic noise sources and their scaling with dimension. This analysis is inspired by potential Bell inequality experiments with superconducting resonator-based qudits. We find that the robustness of the inequality to noise generally decreases with increasing qudit dimension.