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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2412.10305 |
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| _version_ | 1866909044536508416 |
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| author | Slofstra, William Zhang, Lu-Ming |
| author_facet | Slofstra, William Zhang, Lu-Ming |
| contents | We show that if a graph has minimum vertex degree at least d and girth at least g, where (d, g) is (3, 6) or (4, 4), then the incidence system of the graph has a (possibly infinite-dimensional) quantum solution over $\mathbb{Z}_p$ for every choice of vertex weights and integer $p \geq 2$. In particular, there are linear systems over $\mathbb{Z}_p$, for $p$ an odd prime, such that the corresponding linear system nonlocal game has a perfect commuting-operator strategy, but no perfect classical strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator solutions of linear systems and small cancellation Slofstra, William Zhang, Lu-Ming Quantum Physics Combinatorics Group Theory We show that if a graph has minimum vertex degree at least d and girth at least g, where (d, g) is (3, 6) or (4, 4), then the incidence system of the graph has a (possibly infinite-dimensional) quantum solution over $\mathbb{Z}_p$ for every choice of vertex weights and integer $p \geq 2$. In particular, there are linear systems over $\mathbb{Z}_p$, for $p$ an odd prime, such that the corresponding linear system nonlocal game has a perfect commuting-operator strategy, but no perfect classical strategy. |
| title | Operator solutions of linear systems and small cancellation |
| topic | Quantum Physics Combinatorics Group Theory |
| url | https://arxiv.org/abs/2412.10305 |