Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Acta Physica Sinica

Theory of complex ridgelet transform based on the entangled state

Hai-jun Yu, Zhong Guo-Bao, MA Jian-guo, Ren Gang

Published Jan 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.62.174205

Related papers

Ridgelet transform research based on the coordinate representation

Hai-jun Yu, Zhong Guo-Bao, MA Jian-guo +1 more

Inspired by the wavelet transform in quantum mechanics, we define the new Ridgelet transform for quantum optics by rewriting the classic Ridgelet transform via the two-mode coordinate representation in Fock space. Furthermore, we give the explicit form of the asymmetric operator's integral and derive two useful formulas for the normal ordering of the two-mode operator with the help of the technique of integration within an ordered product (IWOP) of operators. By choosing the two-variable Mexican hat's mother wavelet function, we analyse the Ridgelet transforms of the coherent state, special squeezed coherent state, intermediary entangled state on the basis of the theories we have mentioned.

Acta Physica Sinica•Jan 1, 2013•1 citation

Ridgelet transform for quantum optical states

Hai-jun Yu, Zhong Guo-Bao, MA Jian-guo +1 more

We derive a useful formula for the normal ordering of two-mode operator by the technique of integration within an ordered product (IWOP) of operators. Furthermore, we also calculate the Radon transformations for the coherent state, special squeezed coherent state, intermediary entangled state in the view of the quantum mechanics. Based on the results above, the Mexican hat's mother wavelet function is selected to analyse Ridgelet transformations of these three quantum optical states.

Acta Physica Sinica•Jan 1, 2013•1 citation

Application of Bipartite Entangled States to Quantum Mechanical Version of Complex Wavelet Transforms

Fan Hong-Yi, Lu Hai-Liang, Xuefen Xu

We introduce the bipartite entangled states to present a quantum mechanical version of complex wavelet transform. Using the technique of integral within an ordered product of operators we show that the complex wavelet transform can be studied in terms of various quantum state vectors in two-mode Fock space. In this way the creterion for mother wavelet can be examined quantum-mechanically and therefore more deeply.

Communications in Theoretical Physics•Apr 1, 2006•2 citations

Wavelet-Transform Spectrum for Quantum Optical States

Jun Song, Fan Hong‐Yi

In the context of quantum mechanics we employ the technique of integration within an ordered product of operators to recast the classical wavelet transform to a squeezing-displacing transform between the mother wavelet vector and the state vector to be transformed. In this way we propose the wavelet-transform spectrum for quantum optical states. For some typical states we obtain numerical results which imply that the spectrum can be used to recognize a variety of quantum optical states, and the inverse wavelet transform has the possibility to play a role in quantum state engineering.

Chinese Physics Letters•Feb 1, 2010•8 citations

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

Liyun Hu, Fan Hong‐Yi

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

arXiv:0910.5354•Chinese Physics B•Jul 1, 2010•8 citations

Wavelet transform of coherent state

Hai-jun Yu, Jian-ming Du, Xiulan Zhang

Two new mother wavelets are constructed on the basis of the quantum mechanics of classical wavelet transform. Based on that, the wavelet transform of coherent state and particle number state is studied with the technique of integration within an ordered product, and the wavelet transform from coherent state to particle number state is obtained by numerical calculation.

Acta Physica Sinica•Jan 1, 2012•3 citations
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.
Inspired by the wavelet transform in quantum mechanics, we define the new Ridgelet transform for quantum optics by rewriting the classic Ridgelet transform via the two-mode coordinate representation in Fock space. Furthermore, we give the explicit form of the asymmetric operator's integral and derive two useful formulas for the normal ordering of the two-mode operator with the help of the technique of integration within an ordered product (IWOP) of operators. By choosing the two-variable Mexican hat's mother wavelet function, we analyse the Ridgelet transforms of the coherent state, special squeezed coherent state, intermediary entangled state on the basis of the theories we have mentioned.
In the context of quantum mechanics we employ the technique of integration within an ordered product of operators to recast the classical wavelet transform to a squeezing-displacing transform between the mother wavelet vector and the state vector to be transformed. In this way we propose the wavelet-transform spectrum for quantum optical states. For some typical states we obtain numerical results which imply that the spectrum can be used to recognize a variety of quantum optical states, and the inverse wavelet transform has the possibility to play a role in quantum state engineering.