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....
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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147375 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1473752019-02-15T01:25:00Z SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases Albouy, O. Kibler, M.R. 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 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147375 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 |
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 |
| format |
Article |
| author |
Albouy, O. Kibler, M.R. |
| spellingShingle |
Albouy, O. Kibler, M.R. SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Albouy, O. Kibler, M.R. |
| author_sort |
Albouy, O. |
| title |
SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases |
| title_short |
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_sort |
su₂ nonstandard bases: case of mutually unbiased bases |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147375 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:27:11Z |
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