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 |
| Опубліковано: |
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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 |
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