Detecting Full N-Particle Entanglement in Arbitrarily High-Dimensional Systems with Bell-Type Inequality

TL;DR

This paper introduces Bell-type inequalities tailored for high-dimensional systems, providing a method to detect full N-particle entanglement and challenge hybrid local-nonlocal hidden variable models.

Contribution

It derives new Bell-type inequalities applicable to arbitrarily high-dimensional systems, enabling detection of full N-particle entanglement.

Findings

Partially entangled states do not violate the inequalities.

Violations indicate full N-particle entanglement.

Inequalities serve as sufficient conditions for entanglement detection.

Abstract

We derive a set of Bell-type inequalities for arbitrarily high-dimensional systems, based on the assumption of partial separability in the hybrid local-nonlocal hidden variable model. Partially entangled states would not violate the inequalities, and thus upon violation, these Bell-type inequalities are sufficient conditions to detect the full $N$-particle entanglement and validity of the hybrid local-nonlocal hidden variable description.