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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

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          Abstract

          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.

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          Phase properties of the quantized single-mode electromagnetic field

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            UNITARY OPERATOR BASES

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              Quantum systems with finite Hilbert space

              A Vourdas (2004)
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                Author and article information

                Journal
                17 August 2010
                Article
                10.3390/sym2031461
                1008.2881
                853a9d13-8e77-4211-8c79-6624f612e463

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Symmetry 2 (2010) 1461
                quant-ph math-ph math.MP
                ccsd

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