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arXiv · 2501.11826

A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games

Tianshi Yu·Lihong Zhi
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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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Tianshi Yu, Lihong Zhi. 2025-01-21. A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games. https://arxiv.org/abs/2501.11826

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