Range criterion for separability

Horodecki formulated a remarkable criterion for separability, which is called the range criterion. This range criterion was mostly used to show that some states with positive partial transpose are entangled. In this Brief Report, we show that the range criterion is also useful to find a convex combination of product states for a separable state. For this purpose, we give an example of density matrix, which is separable in a 2 x 3 system and entangled in a 3 x 2 system at the same time. Then we illustrate the usefulness of the range criterion with this example.