A new theorem relating quantum tomogram to the Fresnel operator

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 coordinatemomentum representation which is just the eigenvector of the Fresnel quadrature p...

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Published inChinese physics B Vol. 20; no. 6; pp. 19 - 24
Main Author 谢传梅 范洪义
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.06.2011
Subjects
Chaos theory
Density
Formalism
Mathematical analysis
Operators
Representations
Theorems
Wave functions
定理
密度算符
形式主义
断层扫描
特征向量
菲
运营商
量子态
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/20/6/060303

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Summary: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 coordinatemomentum 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 p is equal to the marginal integration of the classical Weyl correspondence function of F1pF, 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.
Bibliography: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 coordinatemomentum 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 p is equal to the marginal integration of the classical Weyl correspondence function of F1pF, 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.
quantum tomogram, Fresnel operator, Weyl correspondence
Xie Chuan-Mei and Fan Hong-Yi（ 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
11-5639/O4
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ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/20/6/060303