The symplectic wavelet transformation proposed in Opt. Lett. 31, 3432 (2006), which is related to the optical Fresnel transform in the quantum optics version, is developed into an entangled symplectic wavelet transformation (ESWT) after pointing out the contrast between the single-mode Fresnel operator and the entangled Fresnel operator. The ESWT possesses well-behaved properties and corresponds to the entangled Fresnel transform [Phys. Lett. A334, 132 (2005)].
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