Maximally entangled states are not complete for pseudo-telepathy

• URL: http://arxiv.org/abs/2608.05378v1
• Date: Wed, 05 Aug 2026 20:00:03 GMT
• Title: Maximally entangled states are not complete for pseudo-telepathy
• Abstract summary: We show a bipartite nonlocal game with input sets of size 4 and 3 and output sets both of size 6.<n>This game is part of a new class of nonlocal games, which we call inner product games, which could be of independent interest.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One of the longstanding open problems in quantum nonlocality is to determine if maximally entangled states are complete for bipartite pseudo-telepathic games: namely, if every nonlocal game which admits a perfect entangled strategy admits such a strategy which uses a maximally entangled state. We exhibit a counterexample to this in the form of a bipartite nonlocal game with input sets of size 4 and 3 and output sets both of size 6. This game is part of a new class of nonlocal games, which we call inner product games, which could be of independent interest.

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