Condition for tripartite entanglement

TL;DR

This paper introduces a classification scheme for tripartite pure qubit states based on hyper-determinants, providing a necessary and sufficient condition for entanglement and separability.

Contribution

It presents a novel classification method using Cayley hyper-determinants and subdeterminants to determine tripartite entanglement.

Findings

Classification scheme with seven elements for tripartite states

Necessary and sufficient condition for separability

Utilizes Cayley hyper-determinant and subdeterminants

Abstract

We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley hyper-determinant, and its six associated $2 \times 2$ subdeterminants. In particular we show that this classification provides a necessary and sufficient condition for separability.