Gisin's Theorem for Arbitrary Dimensional Multipartite States

TL;DR

This paper introduces Bell inequalities that precisely characterize the separability of pure multipartite quantum states in any dimension, linking violation of these inequalities to the states' distillability.

Contribution

It provides a set of Bell inequalities that are both necessary and sufficient for separability in arbitrary dimensions, and explores their relation to quantum state distillability.

Findings

Bell inequalities are necessary and sufficient for pure state separability.

States violating these inequalities are distillable.

The work extends understanding of quantum correlations in high-dimensional multipartite systems.

Abstract

We present a set of Bell inequalities which are sufficient and necessary for separability of general pure multipartite quantum states in arbitrary dimensions. The relations between Bell inequalities and distillability are also studied. We show that any quantum states that violate one of these Bell inequalities are distillable.