Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes
Bell’s theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian , commutative operators corresponding to non-signalin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab2f5b |
| _version_ | 1797750041326125056 |
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| author | Avishy Carmi Yaroslav Herasymenko Eliahu Cohen Kyrylo Snizhko |
| author_facet | Avishy Carmi Yaroslav Herasymenko Eliahu Cohen Kyrylo Snizhko |
| author_sort | Avishy Carmi |
| collection | DOAJ |
| description | Bell’s theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian , commutative operators corresponding to non-signaling observables in Alice’s and Bob’s spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell–Clauser–Horne–Shimony–Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds’ validity yet finding a drastic difference between correlations of ‘signaling’ and ‘non-signaling’ sets of observables. We also propose an experimental procedure for measuring the relevant correlations. |
| first_indexed | 2024-03-12T16:27:06Z |
| format | Article |
| id | doaj.art-0768ee4fa5314b418ac4f33c3054f5e1 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:06Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-0768ee4fa5314b418ac4f33c3054f5e12023-08-08T15:38:47ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121707303210.1088/1367-2630/ab2f5bBounds on nonlocal correlations in the presence of signaling and their application to topological zero modesAvishy Carmi0Yaroslav Herasymenko1Eliahu Cohen2Kyrylo Snizhko3https://orcid.org/0000-0002-7236-6779Center for Quantum Information Science and Technology & Faculty of Engineering Sciences, Ben-Gurion University of the Negev , Beersheba 8410501, IsraelInstituut-Lorentz for Theoretical Physics, Leiden University , Leiden, NL-2333 CA, The NetherlandsFaculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University , Ramat Gan 5290002, IsraelDepartment of Condensed Matter Physics, Weizmann Institute of Science , Rehovot, 76100 IsraelBell’s theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian , commutative operators corresponding to non-signaling observables in Alice’s and Bob’s spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell–Clauser–Horne–Shimony–Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds’ validity yet finding a drastic difference between correlations of ‘signaling’ and ‘non-signaling’ sets of observables. We also propose an experimental procedure for measuring the relevant correlations.https://doi.org/10.1088/1367-2630/ab2f5bBell–CHSH inequalitiesquantum correlationsparafermionsweak measurementssignalingTsirelson bound |
| spellingShingle | Avishy Carmi Yaroslav Herasymenko Eliahu Cohen Kyrylo Snizhko Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes New Journal of Physics Bell–CHSH inequalities quantum correlations parafermions weak measurements signaling Tsirelson bound |
| title | Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes |
| title_full | Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes |
| title_fullStr | Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes |
| title_full_unstemmed | Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes |
| title_short | Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes |
| title_sort | bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes |
| topic | Bell–CHSH inequalities quantum correlations parafermions weak measurements signaling Tsirelson bound |
| url | https://doi.org/10.1088/1367-2630/ab2f5b |
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