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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146777 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862683062216687616 |
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| author | Najarbashi, G. Maleki, Yu. |
| author_facet | Najarbashi, G. Maleki, Yu. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T15:55:13Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146777 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:55:13Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Najarbashi, G. Maleki, Yu. 2019-02-11T14:56:17Z 2019-02-11T14:56:17Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/146777 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems Article published earlier |
| spellingShingle | Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems Najarbashi, G. Maleki, Yu. |
| title | 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_short | Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems |
| title_sort | entanglement of grassmannian coherent states for multi-partite n-level systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146777 |
| work_keys_str_mv | AT najarbashig entanglementofgrassmanniancoherentstatesformultipartitenlevelsystems AT malekiyu entanglementofgrassmanniancoherentstatesformultipartitenlevelsystems |