Three qubit separable states of length ten with unique decompositions

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.