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SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
M. Atakishiyev N., Kibler M. R., Bernardo Wolf K.
Symmetry 2 (2010) 1461 - http://hal.in2p3.fr/in2p3-00510015
Physique/Physique Quantique
Physique/Physique mathématique
Mathématiques/Physique mathématique
SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
Natig M. Atakishiyev, Maurice Robert Kibler ()1, Kurt Bernardo Wolf
1 :  IPNL - Institut de Physique Nucléaire de Lyon
http://www.ipnl.in2p3.fr/
CNRS : UMR5822 – IN2P3 – Université Claude Bernard - Lyon I (UCBL)
France
We propose a group-theoretical approach to the generalized oscillator algebra Ak recently investigated in J. Phys. A: Math. Theor. 43 (2010) 115303. The case k > or 0 corresponds to the noncompact group SU(1,1) (as for the harmonic oscillator and the Poeschl-Teller systems) while the case k < 0 is described by the compact group SU(2) (as for the Morse system). We construct the phase operators and the corresponding temporally stable phase eigenstates for Ak in this group-theoretical context. The SU(2) case is exploited for deriving families of mutually unbiased bases used in quantum information. Along this vein, we examine some characteristics of a quadratic discrete Fourier transform in connection with generalized quadratic Gauss sums and generalized Hadamard matrices.

Articles dans des revues avec comité de lecture
2010
Symmetry
2
1461

03.65.Fd, 03.65.Ta, 03.65.Ud, 02.20.Qs
phase operators – phase states – mutually unbiased bases – discrete Fourier transform
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