The I3322 Bell inequality needs infinite dimensions
Pál–Vértesi conjecture (2010) proved from an approximate proof by GPT-5.5 Pro
Event confirmedAwaiting review
The takeaway
Andrea Coladangelo (University of Washington) proved the Pál–Vértesi conjecture that no finite-dimensional quantum strategy reaches the maximal violation of the I3322 Bell inequality, while an infinite-dimensional one does (arXiv 2609.06038, 5 Sep 2026).
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 30 September 2026
Your AI and this story
- GPT-6 Astra128 days after its cutoff
- Claude Opus 5.567 days after its cutoff
- Gemini 4 Hydrogen158 days after its cutoff
- Grok 4.797 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 67 days before it.
Key facts
- Conjecture: Pál and Vértesi (Physical Review A, 2010); I3322 has three questions and two answers per party, the simplest Bell scenario where this phenomenon could occur
- Previously a 5-question, 3-answer correlation with this property was known (Coladangelo and Stark, Nature Communications 2020)
- Proof tool: a Bellman-function-style certificate from two families of inequalities that bounds the value of any finite-dimensional strategy
- AI usage statement: ‘An approximate proof (containing all of the main ideas) was produced by GPT 5.5 Pro after some rounds of interaction with the author. That first approximate proof was much shorter, and arguably quite difficult to parse by a human’; the final text is the author’s revision, with help from GPT 5.6 Sol
- Status: preprint (78 pages)
What happened
Coladangelo, who had earlier found a larger Bell scenario with the same property, worked with GPT-5.5 Pro on the simplest candidate, I3322. The model produced a terse approximate proof containing the key ideas. The author expanded it into a 78-page rigorous paper.
Why it matters
It settles a basic question about how much entanglement quantum correlations can require, in the smallest possible Bell scenario. It is also one of the clearest 2026 cases of an AI supplying the core idea in quantum foundations.
What is disputed or not yet verified
| Verification | Preprint; not peer-reviewed |
|---|
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
Changes
- Filed