Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U 2 ( μ , σ ) between the mother wavelet vector 〈 ψ | and the two-mode quantum state vector | f 〉 to be transformed. 〈 ψ | U 2 ( μ , σ )| f 〉 can be considered as the spectrum for analyzing the two-mode quantum state | f 〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.