中国物理B ›› 2023, Vol. 32 ›› Issue (4): 40302-040302.doi: 10.1088/1674-1056/ac7e32

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Quantum entangled fractional Fourier transform based on the IWOP technique

Ke Zhang(张科)1, Lan-Lan Li(李兰兰)1, Pan-Pan Yu(余盼盼)1, Ying Zhou(周莹)1, Da-Wei Guo(郭大伟)1, and Hong-Yi Fan(范洪义)2,†   

  1. 1 School of Electronic Engineering, Huainan Normal University, Huainan 232038, China;
    2 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2022-04-06 修回日期:2022-06-14 接受日期:2022-07-05 出版日期:2023-03-10 发布日期:2023-04-04
  • 通讯作者: Hong-Yi Fan E-mail:fhym@ustc.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11775208), the Foundation for Young Talents at the College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077), and the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant Nos. KJ2020A0638 and 2022AH051586).

Quantum entangled fractional Fourier transform based on the IWOP technique

Ke Zhang(张科)1, Lan-Lan Li(李兰兰)1, Pan-Pan Yu(余盼盼)1, Ying Zhou(周莹)1, Da-Wei Guo(郭大伟)1, and Hong-Yi Fan(范洪义)2,†   

  1. 1 School of Electronic Engineering, Huainan Normal University, Huainan 232038, China;
    2 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2022-04-06 Revised:2022-06-14 Accepted:2022-07-05 Online:2023-03-10 Published:2023-04-04
  • Contact: Hong-Yi Fan E-mail:fhym@ustc.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11775208), the Foundation for Young Talents at the College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077), and the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant Nos. KJ2020A0638 and 2022AH051586).

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摘要： 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.

关键词: fractional Fourier transform, coordinate-momentum exchange operators, bivariate operator Hermite polynomial theory, the technique of integration within an ordered product of operators, quantum entangled fractional Fourier transform

Abstract: 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.

Key words: fractional Fourier transform, coordinate-momentum exchange operators, bivariate operator Hermite polynomial theory, the technique of integration within an ordered product of operators, quantum entangled fractional Fourier transform

中图分类号:  (Quantum mechanics)

  • 03.65.-w
42.50.-p (Quantum optics) 63.20.-e (Phonons in crystal lattices)