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A new theorem relating quantum tomogram to the Fresnel operator |
| Xie Chuan-Mei (谢传梅)ab, Fan Hong-Yi (范洪义)b |
| a College of Physics & Material Science, Anhui University, Hefei 230039, China; b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China |
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Abstract According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. 282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.
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Received: 29 June 2010
Revised: 07 March 2011
Accepted manuscript online:
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PACS:
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03.65.Wj
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(State reconstruction, quantum tomography)
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42.50.-p
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(Quantum optics)
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03.65.-w
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(Quantum mechanics)
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| Fund: Project supported by the Doctoral Scientiˉc Research Startup Fund of Anhui University, China (Grant No. 33190059) and the National Natural Science Foundation of China (Grant No. 10874174). |
Cite this article:
Xie Chuan-Mei (谢传梅), Fan Hong-Yi (范洪义) A new theorem relating quantum tomogram to the Fresnel operator 2011 Chin. Phys. B 20 060303
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