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Journal of Physics A: Mathematical and Theoretical 44 (2011) 175303
Finite-dimensional Hilbert space and frame quantization
N. Cotfas1, J.-P. Gazeau2, A. Vourdas

The quantum observables used in the case of quantum systems with finite-dimensional Hilbert space are defined either algebraically in terms of an orthonormal basis and discrete Fourier transformation or by using a continuous system of coherent states. We present an alternative approach to these important quantum systems based on the finite frame quantization. Finite systems of coherent states, usually called finite tight frames, can be defined in a natural way in the case of finite quantum systems. Novel examples of such tight frames are presented. The quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system. They are obtained by using a finite frame and a Klauder-Berezin-Toeplitz-type quantization. Semi-classical aspects of tight frames are studied through lower symbols of basic classical observables.
1 :  Faculty of Physics
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
Physique/Physique mathématique

Mathématiques/Physique mathématique