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Based on the results of constructing the wavelet transform in continuous variable quantum state and the classical continuous ridgelet transform, we construct the continuous complex ridgelet transform in the expression of quantum operators and representations. We study the theory of the complex ridgelet transform in quantum optic state via calculating the inner product and projection of quantum states.
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Keywords:
- technique of integration within an ordered product /
- complex ridgelet transform /
- entangled state /
- coherent state
[1] Candes E J 1999 Ridgelets and Their Derivatives Representation of Images with Edges Department of Statistics, Stanford University, Saint-Malo Proceedings and Larry L. Schumaker(eds), p1-10
[2] Starck J L, Candés E J, Donoho D L 2002 Trans. Image Processing 11 670
[3] Starck J L, Donoho D L, Candes E J 2003 Astronomy & Astrophysics 398 785
[4] Fan H Y, Lu H L 2006 Optics Commun. 258 51
[5] Fan H Y, Lu H L 2006 Opt. Lett. 31 407
[6] Song J, Fan H Y 2010 Chin. Phys. Lett. 27 024210
[7] Fan H Y, Lu H L 2007 Opt. Lett. 32 554
[8] Fan H Y, Liu S G 2007 Opt. Lett. 32 1507
[9] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 147
[10] Song J, Xu Y J, Fan H Y 2011 Acta Phys. Sin. 60 084208 (in Chinese) [宋军, 许业军, 范洪义 2011 60 084208 ]
[11] Yu H J, Du J M, Zhang X L 2012 Acta Phys. Sin. 61 164205 (in Chinese) [余海军, 杜建明, 张秀兰 2012 61 164205]
[12] Fan H Y, Hu L Y 2012 Front. Phys. 7 261
[13] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[14] Fan H Y, Zaidi H R 1988 Phys. Rev. A 37 2985
[15] Fan H Y 2003 Journal of Optics B: Quant. & Semi. Opt. 5 147
[16] Zhou N R, Hu L Y, Fan H Y 2011 Chin. Phys. B 20 120301
[17] Gong L H, Zhou N R, Hu L Y, Fan H Y 2012 Chin. Phys. B 21 080302
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[1] Candes E J 1999 Ridgelets and Their Derivatives Representation of Images with Edges Department of Statistics, Stanford University, Saint-Malo Proceedings and Larry L. Schumaker(eds), p1-10
[2] Starck J L, Candés E J, Donoho D L 2002 Trans. Image Processing 11 670
[3] Starck J L, Donoho D L, Candes E J 2003 Astronomy & Astrophysics 398 785
[4] Fan H Y, Lu H L 2006 Optics Commun. 258 51
[5] Fan H Y, Lu H L 2006 Opt. Lett. 31 407
[6] Song J, Fan H Y 2010 Chin. Phys. Lett. 27 024210
[7] Fan H Y, Lu H L 2007 Opt. Lett. 32 554
[8] Fan H Y, Liu S G 2007 Opt. Lett. 32 1507
[9] Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 147
[10] Song J, Xu Y J, Fan H Y 2011 Acta Phys. Sin. 60 084208 (in Chinese) [宋军, 许业军, 范洪义 2011 60 084208 ]
[11] Yu H J, Du J M, Zhang X L 2012 Acta Phys. Sin. 61 164205 (in Chinese) [余海军, 杜建明, 张秀兰 2012 61 164205]
[12] Fan H Y, Hu L Y 2012 Front. Phys. 7 261
[13] Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[14] Fan H Y, Zaidi H R 1988 Phys. Rev. A 37 2985
[15] Fan H Y 2003 Journal of Optics B: Quant. & Semi. Opt. 5 147
[16] Zhou N R, Hu L Y, Fan H Y 2011 Chin. Phys. B 20 120301
[17] Gong L H, Zhou N R, Hu L Y, Fan H Y 2012 Chin. Phys. B 21 080302
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