The complex fractional Fourier transform, the complex Wigner transform and the entangled Wigner operator in EPR entangled state representation

摘要

Based on the Einstein-Podolsky-Rosen (EPR) entangled state representation, we show that the complex Wigner transform for the complex function psi(eta) turns out to be the quantum statistical average of the entangled Wigner operator in the state |psi >. The complex fractional Fourier transform is also introduced, which corresponds to a rotation of the complex Wigner function. Thus, the intrinsic relation between the complex Wigner transform and the EPR entangled state is revealed.