Non-existence of bipartite bound entanglement with negative partial transposition

TL;DR

This paper proves that bipartite bound entanglement with negative partial transposition (NPT) cannot exist, establishing a fundamental limit on the nature of entangled states in quantum information theory.

Contribution

It demonstrates the non-existence of bipartite NPT bound entanglement, clarifying the structure of entangled states and their distillation properties.

Findings

NPT bound entanglement does not exist.

Any NPT entangled state can be distilled using a finite number of copies.

The minimal Schmidt rank needed for witnessing NPT entanglement is identified.

Abstract

Bound entanglement with a nonpositive partial transposition (NPT) does not exist. For any NPT entangled state a distillation procedure can be based on a certain number of copies. This number is the minimal Schmidt rank of a pure state needed to witness the NPT entanglement under study.