Rank three bipartite entangled states are distillable

TL;DR

This paper proves that all bipartite entangled states of rank three are distillable, establishing that no such states are bound entangled, and explores the distillability of certain rank four states and their relation to Werner states.

Contribution

It demonstrates that bipartite entangled states of rank three are always distillable, filling a gap in understanding entanglement properties based on rank.

Findings

All rank three bipartite entangled states are distillable.

Certain rank four states are also shown to be distillable.

Analysis of the relationship between low rank states and Werner states.

Abstract

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