Relation between quantum tomography and optical Fresnel transform
| dc.creator | Fan, Hong-yi | |
| dc.creator | Hu, Li-yun | |
| dc.date | 2008-01-13 | |
| dc.date.accessioned | 2026-07-07T08:54:14Z | |
| dc.date.available | 2026-07-07T08:54:14Z | |
| dc.description | 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><x| becomes the tomographic density |x>_rs,rs_<x|, which is just the Radon transform of the Wigner operator, i.e., F|x><x|F^(+) = |x>_rs,rs_<x|= \int dx'dp'delta[x-(Dx'-Bp')]*Wigner operator where 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 Wigner function), and the tomogram of a state |phi> is just the wave function of its Fresnel transformed state F|phi>, i.e. rs_<x||phi>= <x|F^(+)|phi>. Similarly, we find F|p><p|F^(+) = |p>_rs,rs_<p|= \int dx'dp'delta[x-(Ap'-Cx')]*Wigner operator. | |
| dc.description | 7 pages, no figure | |
| dc.identifier | https://arxiv.org/abs/0801.1940 | |
| dc.identifier | http://arxiv.org/abs/0801.1940 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145857 | |
| dc.subject | Quantum Physics | |
| dc.title | Relation between quantum tomography and optical Fresnel transform | |
| dc.type | text |