Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure
An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/acb565 |
| _version_ | 1797748727097589760 |
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| author | Hayato Arai Masahito Hayashi |
| author_facet | Hayato Arai Masahito Hayashi |
| author_sort | Hayato Arai |
| collection | DOAJ |
| description | An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose that the local subsystems are fully equal to quantum systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure (SES) is valid. To examine this issue, we introduce pseudo SES as a structure of quantum composite system under natural assumptions based on the existence of projective measurements and the existence of approximations of all maximally entangled standard states. Surprisingly, there exist infinitely many pseudo SESs different from the SES. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure. On the other hand, such pseudo structures never possess global unitary symmetry, i.e. global unitary symmetry is essential condition for the SES. |
| first_indexed | 2024-03-12T16:09:59Z |
| format | Article |
| id | doaj.art-e1be0bfc75554b11a56b91a94f2e6a3b |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:09:59Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e1be0bfc75554b11a56b91a94f2e6a3b2023-08-09T14:12:21ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125202300910.1088/1367-2630/acb565Pseudo standard entanglement structure cannot be distinguished from standard entanglement structureHayato Arai0https://orcid.org/0000-0002-6780-1246Masahito Hayashi1https://orcid.org/0000-0003-3104-1000Graduate School of Mathematics, Nagoya University , Furo-cho, Chikusa-ku, Nagoya 464-8602, JapanGraduate School of Mathematics, Nagoya University , Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology , Nanshan District, Shenzhen 518055, People’s Republic of China; International Quantum Academy (SIQA) , Shenzhen 518048, People’s Republic of China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology , Shenzhen 518055, People’s Republic of ChinaAn experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose that the local subsystems are fully equal to quantum systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure (SES) is valid. To examine this issue, we introduce pseudo SES as a structure of quantum composite system under natural assumptions based on the existence of projective measurements and the existence of approximations of all maximally entangled standard states. Surprisingly, there exist infinitely many pseudo SESs different from the SES. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure. On the other hand, such pseudo structures never possess global unitary symmetry, i.e. global unitary symmetry is essential condition for the SES.https://doi.org/10.1088/1367-2630/acb565general probabilistic theoriesentanglement structureprojective measurementverificationperfect discriminationglobal unitary symmetry |
| spellingShingle | Hayato Arai Masahito Hayashi Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure New Journal of Physics general probabilistic theories entanglement structure projective measurement verification perfect discrimination global unitary symmetry |
| title | Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure |
| title_full | Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure |
| title_fullStr | Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure |
| title_full_unstemmed | Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure |
| title_short | Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure |
| title_sort | pseudo standard entanglement structure cannot be distinguished from standard entanglement structure |
| topic | general probabilistic theories entanglement structure projective measurement verification perfect discrimination global unitary symmetry |
| url | https://doi.org/10.1088/1367-2630/acb565 |
| work_keys_str_mv | AT hayatoarai pseudostandardentanglementstructurecannotbedistinguishedfromstandardentanglementstructure AT masahitohayashi pseudostandardentanglementstructurecannotbedistinguishedfromstandardentanglementstructure |