Symmetry 2010, 2(3), 1461-1484; doi:10.3390/sym2031461
Article

SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms

1, 2,3,4,* email and 5
Received: 9 June 2010; in revised form: 8 July 2010 / Accepted: 9 July 2010 / Published: 12 July 2010
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: We propose a group-theoretical approach to the generalized oscillator algebra Aκ recently investigated in J. Phys. A: Math. Theor. 2010, 43, 115303. The case κ ≥ 0 corresponds to the noncompact group SU(1,1) (as for the harmonic oscillator and the Pöschl-Teller systems) while the case κ < 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 Aκ 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.
Keywords: phase operators; phase states; mutually unbiased bases; discrete Fourier transform
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MDPI and ACS Style

Atakishiyev, N.M.; Kibler, M.R.; Wolf, K.B. SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms. Symmetry 2010, 2, 1461-1484.

AMA Style

Atakishiyev NM, Kibler MR, Wolf KB. SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms. Symmetry. 2010; 2(3):1461-1484.

Chicago/Turabian Style

Atakishiyev, Natig M.; Kibler, Maurice R.; Wolf, Kurt Bernardo. 2010. "SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms." Symmetry 2, no. 3: 1461-1484.

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