Tsirelson Polytopes and randomness generation
We classify the extreme points of a polytope of probability distributions in the (2,2,2) CHSH-Bell setting that is induced by a single Tsirelson bound. We do the same for a class of polytopes obtained from a parametrized family of multiple Tsirelson bounds interacting non-trivially. Such constructio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2020-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aba30d |
| _version_ | 1797750427655077888 |
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| author | Peter Bierhorst Yanbao Zhang |
| author_facet | Peter Bierhorst Yanbao Zhang |
| author_sort | Peter Bierhorst |
| collection | DOAJ |
| description | We classify the extreme points of a polytope of probability distributions in the (2,2,2) CHSH-Bell setting that is induced by a single Tsirelson bound. We do the same for a class of polytopes obtained from a parametrized family of multiple Tsirelson bounds interacting non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors (2018 Phys. Rev. A 98 040304(R)). We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here. |
| first_indexed | 2024-03-12T16:32:32Z |
| format | Article |
| id | doaj.art-82e7d91ba65c43eb830000fe77aac5ab |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:32:32Z |
| publishDate | 2020-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-82e7d91ba65c43eb830000fe77aac5ab2023-08-08T15:25:51ZengIOP PublishingNew Journal of Physics1367-26302020-01-0122808303610.1088/1367-2630/aba30dTsirelson Polytopes and randomness generationPeter Bierhorst0Yanbao Zhang1https://orcid.org/0000-0002-4553-0561Mathematics Department, University of New Orleans , Louisiana, USANTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, NTT Corporation, Atsugi, Kanagawa , JapanWe classify the extreme points of a polytope of probability distributions in the (2,2,2) CHSH-Bell setting that is induced by a single Tsirelson bound. We do the same for a class of polytopes obtained from a parametrized family of multiple Tsirelson bounds interacting non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors (2018 Phys. Rev. A 98 040304(R)). We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here.https://doi.org/10.1088/1367-2630/aba30ddevice-independent random number generationBell nonlocalityTsirelson bounds |
| spellingShingle | Peter Bierhorst Yanbao Zhang Tsirelson Polytopes and randomness generation New Journal of Physics device-independent random number generation Bell nonlocality Tsirelson bounds |
| title | Tsirelson Polytopes and randomness generation |
| title_full | Tsirelson Polytopes and randomness generation |
| title_fullStr | Tsirelson Polytopes and randomness generation |
| title_full_unstemmed | Tsirelson Polytopes and randomness generation |
| title_short | Tsirelson Polytopes and randomness generation |
| title_sort | tsirelson polytopes and randomness generation |
| topic | device-independent random number generation Bell nonlocality Tsirelson bounds |
| url | https://doi.org/10.1088/1367-2630/aba30d |
| work_keys_str_mv | AT peterbierhorst tsirelsonpolytopesandrandomnessgeneration AT yanbaozhang tsirelsonpolytopesandrandomnessgeneration |