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Journal of Mathematical Physics 52 (2011) 082101
Phase operators, phase states and vector phase states for SU(3) and SU(2,1)
Mohammed Daoud1, Maurice Robert Kibler1

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases.
1 :  IPNL - Institut de Physique Nucléaire de Lyon
Physique/Physique Quantique
phase operators – phase states – vector phase states – temporally stable states – generalized harmonic oscillator – su(3) and su(2 – 1) Lie algebras – mutually unbiased bases
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