Completeness of Maximally Entangled States for Pseudo-Telepathy
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Statement
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.
Context
Characterized in the paper as a longstanding open problem of quantum nonlocality, bearing on how much maximal entanglement really buys in nonlocal games.
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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.
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