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SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases
Інший ID:
2000 Mathematics Subject Classification: 81R50; 81R05; 81R10; 81R15
Посилання:
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.
Підтримка:
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.
Дата:
2007
Переглядів:
564
Завантажень:
300
Анотація:
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
