Relation between optical Fresnel transformation and quantum tomography in two-mode entangled case
Hong-Yi Fan, Liyun Hu · Journal of Modern Optics · 2011
Similar in spirit to the preceding work 9 Fan, H-Y and Hu, L-Y. 2009. Opt. Commun., 282: 3734–3736. [Crossref], [Web of Science ®] , [Google Scholar], where the relation between optical Fresnel transformation and quantum tomography is revealed, we explore this kind of relationship in a two-mode entangled case. We show that under the two-mode Fresnel transformation the entangled state density becomes density operator , which is just the Radon transform of the two-mode Wigner operator in entangled form, i.e. where F 2 is a two-mode Fresnel operator in quantum optics, and s , r are the complex-value expressions of (A,B,C,D). So the probability distribution is the tomography (Radon transform of the two-mode Wigner function), and gives a tomogram. Similarly, we find where is the conjugated state to .