SU₂ Nonstandard Bases: Case of Mutually Unbiased Bases

dc.contributor.authorAlbouy, O.
dc.contributor.authorKibler, M.R.
dc.date.accessioned2019-02-14T14:50:37Z
dc.date.available2019-02-14T14:50:37Z
dc.date.issued2007
dc.description.abstractThis 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 appendicesuk_UA
dc.description.sponsorshipThe 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.uk_UA
dc.identifier.citationSU₂ 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.uk_UA
dc.identifier.issn1815-0659
dc.identifier.other2000 Mathematics Subject Classification: 81R50; 81R05; 81R10; 81R15
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/147375
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleSU₂ Nonstandard Bases: Case of Mutually Unbiased Basesuk_UA
dc.typeArticleuk_UA

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