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.
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.