The NPA hierarchy does not always attain the commuting operator value
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909968162095104 |
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| author | Fanizza, Marco Kroell, Larissa Mehta, Arthur Paddock, Connor Rochette, Denis Slofstra, William Zhao, Yuming |
| author_facet | Fanizza, Marco Kroell, Larissa Mehta, Arthur Paddock, Connor Rochette, Denis Slofstra, William Zhao, Yuming |
| contents | We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. Specifically, there is a computable mapping from Turing machines to /boolean constraint system (BCS) nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. As a corollary, there is a BCS game for which the value of the Navascués-Pironio-Acín (NPA) hierarchy does not attain the commuting operator value at any finite level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The NPA hierarchy does not always attain the commuting operator value Fanizza, Marco Kroell, Larissa Mehta, Arthur Paddock, Connor Rochette, Denis Slofstra, William Zhao, Yuming Quantum Physics Computational Complexity We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. Specifically, there is a computable mapping from Turing machines to /boolean constraint system (BCS) nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. As a corollary, there is a BCS game for which the value of the Navascués-Pironio-Acín (NPA) hierarchy does not attain the commuting operator value at any finite level. |
| title | The NPA hierarchy does not always attain the commuting operator value |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2510.04943 |