Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems
In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n>2 degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some well-known entangled pure states, consisting of G...
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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146777 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems / G. Najarbashi, Yu. Maleki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1467772019-02-12T01:23:28Z Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems Najarbashi, G. Maleki, Yu. In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n>2 degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some well-known entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor product of GCSs. It is shown that for three level systems, the Grassmann creation and annihilation operators b and b† together with bz form a closed deformed algebra, i.e., SUq(2) with q=e2πi/3, which is useful to construct entangled qutrit-states. The same argument holds for three level squeezed states. Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled super coherent states. 2011 Article Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems / G. Najarbashi, Yu. Maleki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R30; 15A75; 81P40 DOI:10.3842/SIGMA.2011.011 http://dspace.nbuv.gov.ua/handle/123456789/146777 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n>2 degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some well-known entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor product of GCSs. It is shown that for three level systems, the Grassmann creation and annihilation operators b and b† together with bz form a closed deformed algebra, i.e., SUq(2) with q=e2πi/3, which is useful to construct entangled qutrit-states. The same argument holds for three level squeezed states. Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled super coherent states. |
| format |
Article |
| author |
Najarbashi, G. Maleki, Yu. |
| spellingShingle |
Najarbashi, G. Maleki, Yu. Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Najarbashi, G. Maleki, Yu. |
| author_sort |
Najarbashi, G. |
| title |
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems |
| title_short |
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems |
| title_full |
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems |
| title_fullStr |
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems |
| title_full_unstemmed |
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems |
| title_sort |
entanglement of grassmannian coherent states for multi-partite n-level systems |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146777 |
| citation_txt |
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems / G. Najarbashi, Yu. Maleki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:39Z |
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2023-05-20T17:25:39Z |
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