Generalization of Gisin’s theorem to quantum fields
We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of th...
| Asıl Yazarlar: | , |
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| Materyal Türü: | Makale |
| Dil: | English |
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IOP Publishing
2024-01-01
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| Seri Bilgileri: | New Journal of Physics |
| Konular: | |
| Online Erişim: | https://doi.org/10.1088/1367-2630/ad2821 |
| _version_ | 1827344569984876544 |
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| author | Konrad Schlichtholz Marcin Markiewicz |
| author_facet | Konrad Schlichtholz Marcin Markiewicz |
| author_sort | Konrad Schlichtholz |
| collection | DOAJ |
| description | We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser–Horne (CH) inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the CH inequality. We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics. |
| first_indexed | 2024-03-07T22:49:12Z |
| format | Article |
| id | doaj.art-1aa6e845e212411abe5c1e1a0ceb51f9 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-07T22:49:12Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-1aa6e845e212411abe5c1e1a0ceb51f92024-02-23T11:07:30ZengIOP PublishingNew Journal of Physics1367-26302024-01-0126202304810.1088/1367-2630/ad2821Generalization of Gisin’s theorem to quantum fieldsKonrad Schlichtholz0https://orcid.org/0000-0001-8094-7373Marcin Markiewicz1https://orcid.org/0000-0002-8983-9077International Centre for Theory of Quantum Technologies, University of Gdańsk , 80-309 Gdańsk, PolandInternational Centre for Theory of Quantum Technologies, University of Gdańsk , 80-309 Gdańsk, PolandWe generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser–Horne (CH) inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the CH inequality. We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.https://doi.org/10.1088/1367-2630/ad2821Bell inequalitiesentanglementquantum fieldsFock spaces |
| spellingShingle | Konrad Schlichtholz Marcin Markiewicz Generalization of Gisin’s theorem to quantum fields New Journal of Physics Bell inequalities entanglement quantum fields Fock spaces |
| title | Generalization of Gisin’s theorem to quantum fields |
| title_full | Generalization of Gisin’s theorem to quantum fields |
| title_fullStr | Generalization of Gisin’s theorem to quantum fields |
| title_full_unstemmed | Generalization of Gisin’s theorem to quantum fields |
| title_short | Generalization of Gisin’s theorem to quantum fields |
| title_sort | generalization of gisin s theorem to quantum fields |
| topic | Bell inequalities entanglement quantum fields Fock spaces |
| url | https://doi.org/10.1088/1367-2630/ad2821 |
| work_keys_str_mv | AT konradschlichtholz generalizationofgisinstheoremtoquantumfields AT marcinmarkiewicz generalizationofgisinstheoremtoquantumfields |