Existence of bound entangled states with negative partial transpose (NPT)

Establish whether there exist non-distillable (bound entangled) bipartite states with negative partial transpose (NPT); equivalently, determine whether there exist NPT Werner states in local dimension d > 2 that are nondistillable.

Background

A bipartite state is NPT if its partial transpose has negative eigenvalues. Bound entangled states are entangled yet not distillable by local operations and classical communication. PPT entangled states exist in higher dimensions and are nondistillable, but the existence of NPT bound entanglement is a central unresolved issue.

This question connects to the theory of positive and co-positive maps and can be reduced to Werner states. Proving existence (or nonexistence) would impact entanglement theory, superadditivity phenomena, and properties of distillable entanglement.

References

This is one of the long-standing open questions of quantum information theory.

— Five open problems in quantum information  (2002.03233 - Horodecki et al., 2020) in Section: Quantum entanglement and its distillability; Subsection: Bound entanglement

While it is clear that no maximally entangled state can be created from many copies of a PPT-state it is currently unknown whether the same can be true for an NPPT-state.

— Positivity of linear maps under tensor powers  (1502.05630 - Müller-Hermes et al., 2015) in Section 2 (Notation and preliminaries), paragraph on NPPT-bound entanglement