Combinatorial optical complex wavelet-fractional Fourier transform.

By using the technique of integration within ordered product of operators, we put forward the combinatorial optical complex wavelet-fractional Fourier transform in the context of quantum optics. The unitary operator for this new transform is found and its normally ordered form is deduced. We apply this new transform to the two-mode vacuum state and the two-mode number state and explain that it can be used to analyze and identify various quantum optical states.

New complex integration transformation and its compatibility with complex Weyl-Wigner transformation and entangled state representation.

Enlightened by the special transformation in our preceding paper [J. Mod. Opt. 56, 1227 (2009)], we propose a new complex integration transformation corresponding to two mutually conjugate two-mode entangled states