Quantum Optical Squeezing Transform for Generalizing Fractional Fourier Transform

Abstract

By establishing the relation between the optical scaled fractional Fourier transform (FFT) and quantum mechanical squeezing-rotating operator transform, we employ the bipartite entangled state representation of two-mode squeezing operator to extend the scaled FFT to more general cases, such as scaled complex FFT and entangled scaled FFT. The additivity and eigenmodes are presented in quantum version. The relation between the scaled FFT and squeezing-rotating Wigner operator is studied.