# Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification

## TL;DR

This paper constructs specific three-qubit biseparable states to demonstrate that all classes in a particular partial separability classification are nonempty, clarifying the structure of entanglement.

## Contribution

It provides explicit constructions of seven types of three-qubit biseparable states, confirming the completeness of the classification scheme.

## Key findings

- All classes of biseparable states are nonempty.
- Explicit examples of each class are provided.
- Supports the validity of the partial separability classification.

## Abstract

We construct seven kinds of three-qubit biseparable states to show that every class of biseparable states in the partial separability classification proposed by Szalay and K\"ok\'enyesi [S. Szalay and Z. K\"ok\'enyesi, Phys. Rev. A 86, 032341 (2012)] is nonempty.