Finite-Copy Distillability of NPT States in the DiVincenzo Family
Whether negative-partial-transpose states undistillable from one copy become distillable from finitely many copies is a basic open problem in entanglement theory. In the canonical two-parameter DiVincenzo family used as its symmetry-reduced testbed, a distinguished one-copy-undistillable state is shown to be two-copy distillable in every local dimension d >= 3, disproving the conjecture that the family's whole one-copy-undistillable region stays undistillable for arbitrarily many copies.
- Result
- Disproved(see note)
- Status
- Partial result
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Entanglement theory
- Posed by
- David P. DiVincenzo, Peter W. Shor, John A. Smolin, Barbara M. Terhal, Ashish V. Thapliyal
- Year posed
- 2000
- Years open
- 26y
- Solved
- 2026-08-09
- Model
- GPT-5.6 Thinking
- Vendor
- OpenAI
- Collaborators
- Gelo Noel M. Tabia, Kai-Siang Chen, Min-Hsiu Hsieh
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 30 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Partial deliberately: the NPT bound entanglement problem itself is untouched. What falls is the conjecture about the canonical family, and the paper is explicit that a substantial neighbouring region remains unresolved while another is known two-copy undistillable.
What the AI did
The disclosure lists the specific work: "GNMT acknowledges substantial assistance from OpenAI's ChatGPT, using the GPT-5.6 Thinking model, in the discovery and development of this work. The tool helped with scientific reasoning, the numerical filter search, the derivation of exact two-copy and three-copy certificates, and the organization of the arguments. The interaction was initiated and directed by GNMT." An appendix gives a fuller account of the AI-assisted discovery process.
Verification
A preprint days old. The witnesses are explicit Schmidt-rank-two certificates that the authors independently reconstructed and verified, but no outside party has checked them.
Source
- PaperarXiv