Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics
Abstract Different approaches to quantum gravity converge in predicting the existence of a minimal scale of length. This raises the fundamental question as to whether and how an intrinsic limit to spatial resolution can affect quantum mechanical observables associated to internal degrees of freedom....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-05-01
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| Series: | Communications Physics |
| Online Access: | https://doi.org/10.1038/s42005-023-01229-6 |
| _version_ | 1827939886473150464 |
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| author | Pasquale Bosso Luciano Petruzziello Fabian Wagner Fabrizio Illuminati |
| author_facet | Pasquale Bosso Luciano Petruzziello Fabian Wagner Fabrizio Illuminati |
| author_sort | Pasquale Bosso |
| collection | DOAJ |
| description | Abstract Different approaches to quantum gravity converge in predicting the existence of a minimal scale of length. This raises the fundamental question as to whether and how an intrinsic limit to spatial resolution can affect quantum mechanical observables associated to internal degrees of freedom. We answer this question in general terms by showing that the spin operator acquires a momentum-dependent contribution in quantum mechanics equipped with a minimal length. Among other consequences, this modification induces a form of quantum nonlocality stronger than the one arising in ordinary quantum mechanics. In particular, we show that violations of the Bell inequality can exceed the maximum value allowed in ordinary quantum mechanics, the so-called Tsirelson bound, by a positive-valued function of the momentum operator. We introduce possible experimental settings based on neutron interferometry and quantum contextuality, and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations. |
| first_indexed | 2024-03-13T09:01:14Z |
| format | Article |
| id | doaj.art-1fd188f8462f4512b948470b2593f519 |
| institution | Directory Open Access Journal |
| issn | 2399-3650 |
| language | English |
| last_indexed | 2024-03-13T09:01:14Z |
| publishDate | 2023-05-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Communications Physics |
| spelling | doaj.art-1fd188f8462f4512b948470b2593f5192023-05-28T11:18:56ZengNature PortfolioCommunications Physics2399-36502023-05-01611710.1038/s42005-023-01229-6Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanicsPasquale Bosso0Luciano Petruzziello1Fabian Wagner2Fabrizio Illuminati3University of Lethbridge, Department of Physics and AstronomyDipartimento di Ingegneria Industriale, Università degli Studi di SalernoDipartimento di Ingegneria Industriale, Università degli Studi di SalernoDipartimento di Ingegneria Industriale, Università degli Studi di SalernoAbstract Different approaches to quantum gravity converge in predicting the existence of a minimal scale of length. This raises the fundamental question as to whether and how an intrinsic limit to spatial resolution can affect quantum mechanical observables associated to internal degrees of freedom. We answer this question in general terms by showing that the spin operator acquires a momentum-dependent contribution in quantum mechanics equipped with a minimal length. Among other consequences, this modification induces a form of quantum nonlocality stronger than the one arising in ordinary quantum mechanics. In particular, we show that violations of the Bell inequality can exceed the maximum value allowed in ordinary quantum mechanics, the so-called Tsirelson bound, by a positive-valued function of the momentum operator. We introduce possible experimental settings based on neutron interferometry and quantum contextuality, and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.https://doi.org/10.1038/s42005-023-01229-6 |
| spellingShingle | Pasquale Bosso Luciano Petruzziello Fabian Wagner Fabrizio Illuminati Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics Communications Physics |
| title | Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics |
| title_full | Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics |
| title_fullStr | Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics |
| title_full_unstemmed | Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics |
| title_short | Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics |
| title_sort | spin operator bell nonlocality and tsirelson bound in quantum gravity induced minimal length quantum mechanics |
| url | https://doi.org/10.1038/s42005-023-01229-6 |
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