On Density Operators with Gaussian Weyl Symbols

Patrik Wahlberg

We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process defined on the phase space. We study its covariance and our main result is a formula for the Weyl symbol of the covariance operator, expressed in terms of the Weyl symbol of the covariance operator of the original generalized stochastic process.

Feifei Li, Carol Braun, Anupam Garg

The Weyl-Wigner-Moyal formalism is developed for spin by means of a correspondence between spherical harmonics and spherical-harmonic tensor operators. The exact asymptotic relation among the P , Q , and Weyl symbols is found, and the analogue of the Moyal expansion is developed for the Weyl symbol of the product of two operators in terms of the symbols for the individual operators. It is shown that in the classical limit, the Weyl symbol for a commutator equals i times the Poisson bracket of the corresponding Weyl symbols.

Matteo Campanella, David Jou, Maria Stella Mongiovı̀

C Peltzer, Julius J. Brandstatter

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.