A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games
arXiv:2501.11826
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.
5 pages, submitted to ISSAC 2025