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 coord...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.展开更多
We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions in the Laguerre and the Kautz systems are the eigenvectors of modif...We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions in the Laguerre and the Kautz systems are the eigenvectors of modified Sturm-Liouville operators. The results are further generalized to multiple parameters of one complex variable in both the unit disc and the upper half-plane contexts.展开更多
Based on the Fan-Hu＇s formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states＇ wave function in the intermediate representation, which is just the eigenvector of...Based on the Fan-Hu＇s formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states＇ wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of Fl2pF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.展开更多
Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its application...Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.展开更多
We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps...We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.展开更多
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University, China (Grant No. 33190059)the National Natural Science Foundation of China (Grant No. 10874174)
文摘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.
基金supported by National Natural Science Foundation of China(Grant Nos.11571083,11971178 and 11701597)the starting grant of South China Agricultural Universitythe Science and Technology Development Fund,Macao SAR(Grant Nos.154/2017/A3,079/2016/A2 and FDCT 0123/2018/A3)
文摘We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions in the Laguerre and the Kautz systems are the eigenvectors of modified Sturm-Liouville operators. The results are further generalized to multiple parameters of one complex variable in both the unit disc and the upper half-plane contexts.
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China(Grant No.33190059)the National Natural Science Foundation of China(Grant No.10874174)the President Foundation of Chinese Academy of Sciences
文摘Based on the Fan-Hu＇s formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states＇ wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of Fl2pF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10874174)the President Foundation of the Chinese Academy of Sciences
文摘Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)Key Projects of Huainan Normal University,China(Grant No.2019XJZD04)。
文摘We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.
