Distillability of entangled Werner states for d > 2

Determine whether every entangled Werner state ρ_W^{(p)} on C^d ⊗ C^d with dimension d > 2 and parameter p ∈ [−1,0) is distillable under local operations and classical communication.

Background

Werner states are U⊗U-twirled states characterized by a parameter p, with entangled Werner states corresponding to p ∈ [−1,0). For d = 2, all entangled Werner states are known to be distillable.

For d > 2, it remains unresolved whether all entangled Werner states are distillable. This question is central in entanglement theory and interacts with the authors’ distillation-based techniques used to analyze tensor-stable positive maps.

References

But for $d>2$ it is not known whether all entangled Werner states are distillable.

— Positivity of linear maps under tensor powers  (1502.05630 - Müller-Hermes et al., 2015) in Appendix A (Twirling and families of symmetric matrices)