Self-testing tilted strategies for maximal loophole-free nonlocality
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912421081251840 |
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| author | Gigena, Nicolas Panwar, Ekta Scala, Giovanni Araújo, Mateus Farkas, Máté Chaturvedi, Anubhav |
| author_facet | Gigena, Nicolas Panwar, Ekta Scala, Giovanni Araújo, Mateus Farkas, Máté Chaturvedi, Anubhav |
| contents | The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the doubly-tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. We utilize a Jordan's lemma and Gröbner basis-based proof technique to analytically derive self-testing statements for the entire family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the Navascués--Pironio--Acín hierarchy to saturate the maximum quantum violation of these inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-testing tilted strategies for maximal loophole-free nonlocality Gigena, Nicolas Panwar, Ekta Scala, Giovanni Araújo, Mateus Farkas, Máté Chaturvedi, Anubhav Quantum Physics The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the doubly-tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. We utilize a Jordan's lemma and Gröbner basis-based proof technique to analytically derive self-testing statements for the entire family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the Navascués--Pironio--Acín hierarchy to saturate the maximum quantum violation of these inequalities. |
| title | Self-testing tilted strategies for maximal loophole-free nonlocality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.08743 |