Three-qubit entanglement witnesses with the full spanning properties

TL;DR

This paper introduces three-qubit entanglement witnesses with full spanning properties, capable of detecting PPT entangled states and bi-separable states, advancing the understanding of multipartite entanglement detection.

Contribution

It constructs novel entanglement witnesses with spanning properties for all partial transposes, enabling detection of a broader class of entangled states in three-qubit systems.

Findings

Detects PPT entangled states with nonempty interiors

Identifies all bi-separable pure product states

Constructs witnesses based on positive multi-linear maps

Abstract

We construct three-qubit entanglement witnesses with the properties that all the partial transposes have the spanning properties. These witnesses determine faces for separable states whose interior lies in the interior of PPT states, and so they detect sets of PPT entangled states with nonempty interiors. These witnesses also detect all kinds of bi-separable pure product states. Our construction depends on the observation that multi-partite entanglement witnesses correspond to multi-linear maps which are positive.