SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases
This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU₂ corresponding to an irreducible representation of SU₂. The representation theory of SU₂ is reconsidered via the use of two truncated deformed oscillators....
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147375 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases / O. Albouy, M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 78 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862539424864141312 |
|---|---|
| author | Albouy, O. Kibler, M.R. |
| author_facet | Albouy, O. Kibler, M.R. |
| citation_txt | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases / O. Albouy, M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 78 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU₂ corresponding to an irreducible representation of SU₂. The representation theory of SU₂ is reconsidered via the use of two truncated deformed oscillators. This leads to replacement of the familiar scheme {j²,jz} by a scheme {j²,vra}, where the two-parameter operator vra is defined in the universal enveloping algebra of the Lie algebra su₂. The eigenvectors of the commuting set of operators {j²,vra} are adapted to a tower of chains SO₃⊃C₂j₊₁ (2j∈N∗), where C₂j₊₁ is the cyclic group of order 2j+1. In the case where 2j+1 is prime, the corresponding eigenvectors generate a complete set of mutually unbiased bases. Some useful relations on generalized quadratic Gauss sums are exposed in three appendices
|
| first_indexed | 2025-11-24T15:15:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147375 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T15:15:40Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Albouy, O. Kibler, M.R. 2019-02-14T14:50:37Z 2019-02-14T14:50:37Z 2007 SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases / O. Albouy, M.R. Kibler // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 78 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R50; 81R05; 81R10; 81R15 https://nasplib.isofts.kiev.ua/handle/123456789/147375 This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU₂ corresponding to an irreducible representation of SU₂. The representation theory of SU₂ is reconsidered via the use of two truncated deformed oscillators. This leads to replacement of the familiar scheme {j²,jz} by a scheme {j²,vra}, where the two-parameter operator vra is defined in the universal enveloping algebra of the Lie algebra su₂. The eigenvectors of the commuting set of operators {j²,vra} are adapted to a tower of chains SO₃⊃C₂j₊₁ (2j∈N∗), where C₂j₊₁ is the cyclic group of order 2j+1. In the case where 2j+1 is prime, the corresponding eigenvectors generate a complete set of mutually unbiased bases. Some useful relations on generalized quadratic Gauss sums are exposed in three appendices The senior author (M.R.K.) acknowledges Philippe Langevin for useful correspondence. The authors thank Hubert de Guise, Michel Planat, and Metod Saniga for interesting discussions. They are indebted to Bruce Berndt and Ron Evans for providing them with an alternative proof of the result in Appendix C. Thanks are due to the Referees for useful and constructive suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases Article published earlier |
| spellingShingle | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases Albouy, O. Kibler, M.R. |
| title | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases |
| title_full | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases |
| title_fullStr | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases |
| title_full_unstemmed | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases |
| title_short | SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases |
| title_sort | su₂ nonstandard bases: case of mutually unbiased bases |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147375 |
| work_keys_str_mv | AT albouyo su2nonstandardbasescaseofmutuallyunbiasedbases AT kiblermr su2nonstandardbasescaseofmutuallyunbiasedbases |