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

Communications in Theoretical Physics

Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation

Qian Xiao-Qing, Song Tong-Qiang

Published Jun 1, 2006• 1 citation
Publisher

Abstract

We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n -mode entangled states of continuum variables in n -mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n -mode squeezed state.

DOI
10.1088/0253-6102/45/6/026

Related papers

On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Fan Hong‐Yi, Nian-Quan Jiang

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variables in three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled state representations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained, which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.

Communications in Theoretical Physics•Jul 15, 2003•8 citations

On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

FANHong-Yi, JIANGNian-Quan

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variables in three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled state representations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.

理论物理通讯：英文版•Jan 1, 2003•0 citations

On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Fan Fan, Hong-Yi, Jiang +1 more

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.

理论物理通讯：英文版•Jan 1, 2003•2 citations

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

吕翠红 L Cui-hong, Fan Hong‐Yi, Nian-Quan Jiang

We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation (EFFT) and derive the transformation kernel. The EFFT's additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

Chinese Physics B•Dec 1, 2010•7 citations

NEW n-MODE BOSE OPERATOR REALIZATION OF SU(2) LIE ALGEBRA AND ITS APPLICATION IN ENTANGLED FRACTIONAL FOURIER TRANSFORM

Hong-Yi Fan, Shuguang Liu

We introduce a new n-mode Bose operator realization of SU(2) Lie algebra and link it to the two mutually conjugate multipartite entangled state representations. In so doing we are naturally lead to the n-mode entangle fractional Fourier transform (EFFT), which provides us with a convenient way to deriving the EFFT of quantum-mechanical wave functions.

Modern Physics Letters A•Mar 14, 2009•6 citations

Quantum entangled fractional Fourier transform based on the IWOP technique

Ke Zhang, Lanlan Li, Pan-Pan Yu +3 more

In our previous papers, the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics, and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform. The core function of the coordinate–momentum exchange operators in the addition law of fractional Fourier transform was analyzed too. In this paper, the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators (IWOP) are used to establish the entanglement fractional Fourier transform theory to the extent of quantum. A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Chinese Physics B•Jul 5, 2022•4 citations
We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n -mode entangled states of continuum variables in n -mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n -mode squeezed state.
In our previous papers, the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics, and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform. The core function of the coordinate–momentum exchange operators in the addition law of fractional Fourier transform was analyzed too. In this paper, the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators (IWOP) are used to establish the entanglement fractional Fourier transform theory to the extent of quantum. A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.