The quantum smooth label cover problem is undecidable
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917062207602688 |
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| author | Culf, Eric Mastel, Kieran Paddock, Connor Spirig, Taro |
| author_facet | Culf, Eric Mastel, Kieran Paddock, Connor Spirig, Taro |
| contents | We show that the quantum smooth label cover problem is undecidable and RE-hard. This sharply contrasts the quantum unique label cover problem, which can be decided efficiently by a result of Kempe, Regev, and Toner (FOCS'08). On the other hand, our result aligns with the RE-hardness of the quantum label cover problem, which follows from the celebrated MIP* = RE result of Ji, Natarajan, Vidick, Wright, and Yuen (ACM'21). Additionally, we show that the quantum oracularized smooth label cover problem is RE-hard. Our second result fits with the alternative quantum unique games conjecture recently proposed by Mousavi and Spirig (ITCS'25) on the RE-hardness of the quantum oracularized unique label cover problem. Our proof techniques include a quantum version of Feige's reduction from 3SAT to 3SAT5 (STOC'96) for BCSMIP*-protocols, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantum smooth label cover problem is undecidable Culf, Eric Mastel, Kieran Paddock, Connor Spirig, Taro Quantum Physics We show that the quantum smooth label cover problem is undecidable and RE-hard. This sharply contrasts the quantum unique label cover problem, which can be decided efficiently by a result of Kempe, Regev, and Toner (FOCS'08). On the other hand, our result aligns with the RE-hardness of the quantum label cover problem, which follows from the celebrated MIP* = RE result of Ji, Natarajan, Vidick, Wright, and Yuen (ACM'21). Additionally, we show that the quantum oracularized smooth label cover problem is RE-hard. Our second result fits with the alternative quantum unique games conjecture recently proposed by Mousavi and Spirig (ITCS'25) on the RE-hardness of the quantum oracularized unique label cover problem. Our proof techniques include a quantum version of Feige's reduction from 3SAT to 3SAT5 (STOC'96) for BCSMIP*-protocols, which may be of independent interest. |
| title | The quantum smooth label cover problem is undecidable |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.03477 |