The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and homogenous space, and the quantum entanglement description using group theory were both studied in our previous articles. Here, we present a universal description of quantum entanglement using group theory and non-commutative characteristic functions for homogenous space and projective representation of compact groups on Banach spaces for some well known examples, such as: Moyal representation for a spin; Dihedral and Permutation groups.
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