A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games

• URL: http://arxiv.org/abs/2501.11826v2
• Date: Sat, 25 Jan 2025 01:43:59 GMT
• Title: A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games
• Authors: Tianshi Yu, Lihong Zhi,
• Abstract summary: We prove that a two-answer nonlocal game with a perfect quantum strategy also admits a perfect classical strategy. This result induces a special case of noncommutative Nullsatz.
• Score: 0.0
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• 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.

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