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Similar in spirit to the preceding work [Opt. Commun. 282 (2009) 3734] wherethe relation between optical Fresnel transformation and quantum tomography isrevealed, we study this kind of relationship in the two-mode entangled case. Weshow that under the two-mode Fresnel transformation the bipartite entangledstate density |eta><eta| becomes density operator F_2|eta><eta|F_2^{dag}=|eta>_{r,s}<eta|, which is just the Radon transform of the two-modeWigner operator (sigma,gama) in entangled form, where F_2 is an two-modeFresnel operator in quantum optics, and s,r are the complex-value expression of(A, B, C,D). So the probability distribution for the Fresnel quadrature phaseis the {tomography (Radon transform of the two-mode Wigner function),correspondingly, {s,r}_<eta|phi>=<eta|F_2{dag}|phi>. Similarly, we find asimial conclusion in the `frequency` domain.

Relation between Optical Fresnel transformation and quantum tomography in two-mode entangled case