Relation between Optical Fresnel transformation and quantum tomography in two-mode entangled case
Abstract
Similar in spirit to the preceding work [Opt. Commun. 282 (2009) 3734] where the relation between optical Fresnel transformation and quantum tomography is revealed, we study this kind of relationship in the two-mode entangled case. We show that under the two-mode Fresnel transformation the bipartite entangled state 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-mode Wigner operator (sigma,gama) in entangled form, where F_2 is an two-mode Fresnel 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 phase is the {tomography (Radon transform of the two-mode Wigner function), correspondingly, {s,r}_<eta|phi>=<eta|F_2{dag}|phi>. Similarly, we find a simial conclusion in the `frequency` domain.
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Cite
@article{arxiv.0911.1596,
title = {Relation between Optical Fresnel transformation and quantum tomography in two-mode entangled case},
author = {Hong-yi Fan and Li-yun Hu},
journal= {arXiv preprint arXiv:0911.1596},
year = {2009}
}
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10 pages