NPT bound entanglement

Entanglement distillation converts many copies of a noisy entangled state into near-perfect Bell pairs by local operations and classical communication (LOCC). A state with positive partial transpose (PPT) cannot be distilled. The reverse question — whether every negative-partial-transpose (NPT) state is distillable — remains a foundational open problem.

What is known: All NPT states in $2\times n$ systems are distillable. The general existence question reduces to the Werner-state benchmark retained at E2. For $\rho_\alpha=(I+\alpha F)/(d^2+\alpha d)$, with $F$ the swap operator, the NPT but one-copy-undistillable interval is $-1/2\leq\alpha<-1/d$ for $d\geq3$. A fixed state in this interval undistillable for every copy number would establish NPT bound entanglement. Finite-copy results and numerical evidence apply to specified parameters and copy numbers; they do not establish all-copy undistillability of one NPT state. Three July 2026 preprints claim coincident one-copy and two-copy thresholds; E2 preserves the details and partial three-copy results.

Preprint progress (August 2026): Tabia, Chen and Hsieh report that a distinguished one-copy-undistillable state in the two-parameter DiVincenzo family is two-copy distillable in every local dimension $d\geq3$. Their witnesses cover a neighborhood, and further three-copy witnesses enlarge the distillable region. This addresses that family's proposed undistillable region, not the Werner conjecture or general NPT question. Independent proof verification is not claimed here.

NPT bound entanglement would have major consequences for activation and the nonadditivity of distillability. A single explicit all-copy-undistillable NPT state, or a proof that no such state exists, resolves the question.

Source review dated 4 September 2026. “Improved” records partial progress and may include preprint claims; it does not mean the problem has been solved.

preprint: Two-copy distillation is claimed for a distinguished state and neighborhoods in the two-parameter DiVincenzo family, not the general Werner or NPT problem. Evidence