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A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games (2501.11826v2)
Published 21 Jan 2025 in quant-ph and math.OA
Abstract: This paper introduces a noncommutative version of the Nullstellensatz, motivated by the study of quantum nonlocal games. It has been proved that a two-answer nonlocal game with a perfect quantum strategy also admits a perfect classical strategy. We generalize this result to the infinite-dimensional case, showing that a two-answer game with a perfect commuting operator strategy also admits a perfect classical strategy. This result induces a special case of noncommutative Nullstellensatz.