Do bound entangled states with a negative partial transpose exist?

Unresolved.

Every distillable state is NPT. Is the converse true? In dimensions above 2×2, evidence going back to 1999 suggests some NPT states may be undistillable, with Werner states the central family under study.

Still unknown

It remains listed among the five open problems of Horodecki, Rudnicki and Życzkowski, and a 2024 paper still calls it long-standing. A 2006 preprint claimed existence, but later work continues to treat the question as open.

Connections

Part of: Conversion
See also: Bound entanglement exists
See also: Can distillable entanglement be computed in general?
See also: Every entangled two-qubit state is distillable
Narrowed by: NPT Werner states are two-copy undistillable in every dimension

Sources

Evidence for bound entangled states with negative partial transpose. D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, A. V. Thapliyal, 1999.
Distillability and partial transposition in bipartite systems. W. Dür, J. I. Cirac, M. Lewenstein, D. Bruss, 1999.
Five open problems in quantum information. P. Horodecki, Ł. Rudnicki, K. Życzkowski, 2020.
Unveiling NPT bound problem: from distillability sets to inequalities and multivariable insights. S.-Y. Qi, G. Gupur, Y.-C. Wu, G.-P. Guo, 2024.
NPPT bound entanglement exists. R. Simon, 2006.

Checked 2026-10-30.