Three qubit separable states of length ten with unique decompositions

TL;DR

This paper constructs specific three-qubit separable states of length ten with unique decompositions, located on the boundary of the separable set but inside the PPT states, advancing understanding of quantum state structure.

Contribution

It introduces a family of three-qubit separable states with length ten, exceeding the dimension, and demonstrates their unique convex decompositions and boundary positioning.

Findings

States have length ten, greater than the dimension eight.

States are on the boundary of separable states but inside PPT states.

States have unique convex decompositions into ten pure product states.

Abstract

We construct one parameter families of three qubit separable states with length ten, which is strictly greater than the whole dimension eight. These states are located on the boundary of the convex set of all separable states, but they are in the interior of the convex set of all states with positive partial transposes. They are also decomposed into the convex sum of ten pure product states in a unique way.