Optical Fresnel transformation and quantum tomography

Margarita A. Man’ko, Sergio M. De Nicola, Renato Fedele +1 more

Hong-Yi Fan, Xubing Tang, Lu Hai-Liang

Giacomo Mauro D’Ariano, Lorenzo Maccone

Hong-Yi Fan, Liyun Hu

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 .

Giacomo Mauro D’Ariano, Matteo G. A. Paris, Massimiliano Federico Sacchi

Hong-Yi Fan, Liyun Hu

Corresponding to optical Fresnel transformation characteristic of ray transfer matrix elements (A;B;C;D); AD-BC = 1, there exists Fresnel operator F(A;B;C;D) in quantum optics, we show that under the Fresnel transformation the pure position density |x>_rs,rs__rs,rs_ is just the wave function of its Fresnel transformed state F|phi>, i.e. rs_= . Similarly, we find F|p>_rs,rs_