Completeness of Maximally Entangled States for Pseudo-Telepathy
Does every nonlocal game admitting a perfect entangled strategy admit one using a maximally entangled state? Described in the paper as one of the longstanding open problems in quantum nonlocality. Answered negatively by an explicit counterexample game.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Computation
- Field
- Quantum nonlocality
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-08-05
- Model
- Codex
- Vendor
- OpenAI
- Collaborators
- Olivier Lalonde
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 22 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The author is emphatic that the ideas are his: "AI tools were used extensively during the course of this work, but only as a means of executing ideas rather than producing them." What Codex did do is decisive rather than cosmetic: it searched for the matrix making the game classically infeasible, implemented the pruning, and implemented and ran a strengthened tracial NPA hierarchy that demonstrated the nonexistence of the required tracial state, completing the proof of Theorem 1.1 and extracting a rational infeasibility certificate.
Verification
A preprint days old. The decisive step is a semidefinite-programming infeasibility certificate, machine-produced and rational, so it is checkable in principle; nobody independent has checked it.