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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11826 |
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| _version_ | 1866929686145138688 |
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| author | Yu, Tianshi Zhi, Lihong |
| author_facet | Yu, Tianshi Zhi, Lihong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games Yu, Tianshi Zhi, Lihong Quantum Physics Operator Algebras 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. |
| title | A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games |
| topic | Quantum Physics Operator Algebras |
| url | https://arxiv.org/abs/2501.11826 |