SWhat changed
Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets.
Scientific scope
Paweł Horodecki constructed explicit entangled states with positive partial transpose in 3x3 and 2x4 dimensions using a range criterion. The 1998 Horodecki paper proves that distillability requires a negative partial transpose: PPT states remain PPT under tensor powers and local operations with classical communication, hence these entangled states cannot be distilled into singlets. The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The 1997 construction has a sole-author byline; the 1998 nondistillability theorem has three authors. The converse that every NPT state is distillable is not proved. Bound entanglement here means no singlet distillation under the specified operations, not no possible use in every communication, privacy or activation task.
Contributors
- The named authors in the research record · SCIENCE: The original named human researchers developed the exact mathematical construction or framework. Composite source families retain separate original paper bylines and predecessor roles; they are not a fictional joint publication. Individual effort shares, person identity joins and nationalities are not inferred. The source reading is not independent proof certification.
- Separability criterion and inseparable mixed states with positive partial transposition
- Mixed-state entanglement and distillation: is there a bound entanglement in nature?
Provisional WRS assessment, edition 2026-10-23.9. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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