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Abstract
We demonstrate that the complex fractional Fourier transformation (CFRFT) can be deduced by two-mode SU(2) quadratic canonical operators and bipartite-entangled state representations. It turns out that the CFRFT is a special case of the two-dimensional (2D) complex Fresnel transformation, just as the 1D fractional Fourier transformation is adapted to the 1D Fresnel transformation.
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