Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies

TL;DR

This paper explores the construction of geometrical Bell inequalities for GHZ states across arbitrary dimensions, aiming to understand their nonclassical behavior and robustness compared to other inequalities.

Contribution

It introduces new strategies for formulating geometrical Bell inequalities applicable to GHZ states of any dimension, extending previous results beyond qubits.

Findings

Geometrical Bell inequalities show increased robustness for GHZ states in higher dimensions.

Different outcome strategies influence the strength of Bell inequality violations.

The work generalizes Bell inequality constructions to arbitrary qudit systems.

Abstract

Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown that GHZ states lead to more robustness of Bell nonclassicality in case of geometrical inequalities than in case of Mermin inequalities. We investigate various strategies of constructing geometrical Bell inequalities (BIs) for GHZ states for any dimensionality of subsystems.