Geodesic
Convolution theorem for the~three-dimensional entangled fractional Fourier transformation deduced from the~tripartite entangled state representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 459-468

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We find that constructing the two mutually-conjugate tripartite entangled state representations naturally leads to the entangled Fourier transformation. We then derive the convolution theorem for the three-dimensional entangled fractional Fourier transformation in the context of quantum mechanics.
Keywords: three-dimensional entangled fractional Fourier transformation, convolution theorem, tripartite entangled state representation. 
@article{TMF_2009_161_3_a10,
     author = {Shu-guang Liu and Hong-yi Fan},
     title = {Convolution theorem for the~three-dimensional entangled fractional {Fourier} transformation deduced from the~tripartite entangled state representation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {459--468},
     publisher = {mathdoc},
     volume = {161},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a10/}
}
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Shu-guang Liu; Hong-yi Fan. Convolution theorem for the~three-dimensional entangled fractional Fourier transformation deduced from the~tripartite entangled state representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 459-468. http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a10/