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

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Abstract

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 η| and ξ| that is compatible with ηξ phase space quantum mechanics and can be used to obtain the complex fractional Fourier transformation kernel from the chirplet function. This transformation obeys the Parseval theorem and is invertible.

© 2009 Optical Society of America

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