Application of Fourier Slice Theorem in Wigner Operator Theory and New Complete Representation

Ryogo Hirota, Soitiro Tosima

Wang Tong-Tong, Fan Hong‐Yi

By applying the Fourier slice theorem, , where P θ (t) is a projection of along lines of constant, to the Wigner operator we are naturally led to a projection operator (pure state), which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.

Ke Zhang, H. C. Fan

The Wigner operator’s normal ordering form is deduced by using the method of integration within the ordered product of operators, and the operator’s Weyl ordering symbol is employed. The integration theory within the Weyl ordering product of operators is applied, and the Wigner operator’s Weyl ordering form is deduced. Then, the Wigner operator’s slice theorem is proposed, which helps project and display a new pure-state density operator. Thus, the quantization of classical tomography theory is realized. We illustrate the derivation of the bi- and tri-partite entangled state representations, respectively, which completes the argument.

Demosthenes Ellinas, I. Tsohantjis

Wang Tong-Tong, Hong-Yi Fan

Using the Weyl quantization scheme and based on the Fourier slice transformation (FST) of the Wigner operator, we construct a new expansion formula of the density operator ρ, with the expansion coefficient being the FST of ρ's classical Weyl correspondence, and the latter the Fourier transformation of ρ's quantum tomogram. The coordinate-momentum intermediate representation is used as the Radon transformation of the Wigner operator.

В. В. Ежела