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Updated: Jun 25, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Symplectic-dilation mixed wavelet transform and its correspondence in quantum optics
Hong-Yi Fan1, Shu-Guang Liu, Li-Yun Hu
1Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui, China.
Abstract:
The symplectic wavelet transform, which is related to the quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable dilation-transform and a complex-variable symplectic transform and possesses well-behaved properties such as the Parseval theorem and the inversion formula. The entangled-coherent state representation not only underlies the SDWT but also helps to derive the corresponding quantum transform operator whose counterpart in classical optics is the lens-Fresnel mixed transform.
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