Two-Copy Distillability of Werner States
Is a Werner state that is not one-copy distillable ever two-copy distillable? The first open rung of the NPT bound-entanglement ladder, open since 2000.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Entanglement theory
- Posed by
- —
- Year posed
- 2000
- Years open
- 26y
- Solved
- 2026-07-23
- Model
- GPT-5.5, GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 35 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Two-copy distillable if and only if already one-copy distillable.
Four independent papers settled this within five days of each other, and no single one of them is the account of record. Fu, Gao and Park posted first on 23 July (arXiv:2607.21367), followed by Song and Chen on 26 July (arXiv:2607.23416), then on 27 July both Fraser, Huber, Pozsgay and Vona (arXiv:2607.24309) and Bharti, Gajjala and Haug (arXiv:2607.24479). The headline axes here follow the first posting, which is a filing convention and not a claim about who solved it.
Pozsgay has stated publicly that his group had their AI-assisted proof before the first paper appeared. This site cannot verify a private completion date, so that is recorded as his account rather than as a finding. All four are linked below.
What the AI did
The proof by Fu, Gao and Park was AI-assisted and independently verified by the authors.
Verification
Author-verified arXiv preprint. Within days, two further groups posted independent proofs of the same theorem (arXiv:2607.24309, arXiv:2607.24479), which strengthens confidence but none is yet peer-reviewed.
Sources
- PaperarXiv:2607.21367 - A solution to 2-copy distillability of Werner states
- Independent workSong and Chen - A partial-trace matrix inequality and Werner-state distillability (26 Jul)Fraser, Huber, Pozsgay and Vona - two-copy distillability and a new partial trace bound (27 Jul)Bharti, Gajjala and Haug - sharp partial-trace inequalities (27 Jul)
This should probably be listed as "proved", not "disproved". The conjecture in quantum information theory is that these states are bound entangled, which implies that they are two-copy undistillable. This proof makes progress on that conjecture, rather than refuting it.