On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangledstates of continuum variables in three-mode Fock space we introduceentangled fractional Fourier transform (EFFT) for the tripartite entangledstate representations, which are not a direct product of three 1-dimensionalFFTs. The eigenmodes of EFFT are obtained, which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.