We prove that rank-three bipartite entangled states are distillable. So there are no bound rank-three bipartite entangled states. By using this fact, we present some families of rank-four states that are distillable. We also analyze the relation between the rank-three state and the Werner state.

• Received 6 March 2008

DOI:https://doi.org/10.1103/PhysRevA.78.022318