Physics – Quantum Physics
Scientific paper
2007-01-30
SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 3 (2007) 076
Physics
Quantum Physics
33 pages; version2: rescaling of generalized Hadamard matrices, acknowledgment and references added, misprints corrected; vers
Scientific paper
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 SU(2) corresponding to an irreducible representation of SU(2). The representation theory of SU(2) is reconsidered via the use of two truncated deformed oscillators. This leads to replace the familiar scheme {j^2, j_z} by a scheme {j^2, v(ra)}, where the two-parameter operator v(ra) is defined in the enveloping algebra of the Lie algebra su(2). The eigenvectors of the commuting set of operators {j^2, v(ra)} are adapted to a tower of chains SO(3) > C(2j+1), 2j integer, where C(2j+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.
Albouy Olivier
Kibler Maurice R.
No associations
LandOfFree
SU(2) nonstandard bases: the case of mutually unbiased bases does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with SU(2) nonstandard bases: the case of mutually unbiased bases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and SU(2) nonstandard bases: the case of mutually unbiased bases will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-470885