Abstract
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.
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References
Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelphia (1992)
Chui, C.K.: An Introduction to Wavelets. Academic Press, New York (1992)
Burrus, C.S., Gopinath, R.A., Guo, H.T.: Introduction to Wavelets and Wavelet Transformation (A Primer). Prentice-Hall, New Jersey (1998)
Pinsky, M.A.: Introduction to Fourier Analysis and Wavelets. Brooks/Cole, Sydney (2002)
Song, J., Fan, H.Y., Xu, Y.J., Zhou, J.: Int. J. Theor. Phys. 50, 1492 (2011)
Fan, H.Y., Klauder, J.R.: Phys. Rev. A 49, 704 (1994)
Fan, H.Y., Ye, X.: Phys. Rev. A 51, 3343 (1995)
Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)
Fan, H.Y., Lu, H.L.: Opt. Lett. 31, 407 (2006)
Fan, H.Y., Lu, H.L.: Opt. Lett. 32, 554 (2007)
Fan, H.Y., Zaidi, H.R., Klauder, J.R.: Phys. Rev. D 35, 1831 (1987)
Fan, H.Y., Zaidi, H.R.: Phys. Rev. A 37, 2985 (1988)
Fan, H.Y., VanderLinde, J.: Phys. Rev. A 39, 1552 (1989)
Song, J., Fan, H.Y.: Chin. Phys. Lett. 27, 024210 (2010)
Song, J., Fan, H.Y.: Int. J. Theor. Phys. 49, 2582 (2010)
Glauber, R.J.: Phys. Rev. 130, 2529 (1963)
Glauber, R.J.: Phys. Rev. 131, 2766 (1963)
Klauder, J.R., Skargerstam, B.S.: Coherent States. World Scientific, Singapore (1985)
Louisell, W.H.: Quantum Statistical Properties of Radiation. Wiley, New York (1973)
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Work supported by the provincial natural science research program of higher education institutions of Anhui province under Grants KJ2013A258 and KJ2013A261.
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Song, J., Zhou, J., Yuan, H. et al. Complex Wavelet Transform of the Two-mode Quantum States. Int J Theor Phys 55, 3597–3606 (2016). https://doi.org/10.1007/s10773-016-2988-9
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DOI: https://doi.org/10.1007/s10773-016-2988-9