Quantum entangled fractional Fourier transform based on the IWOP technique

doi:10.1088/1674-1056/ac7e32

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.

Keywords: 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

Received: 06 April 2022
Revised: 14 June 2022
Accepted manuscript online: 05 July 2022

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

Fund: 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).

Corresponding Authors: Hong-Yi Fan
E-mail: fhym@ustc.edu.cn

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Ke Zhang(张科), Lan-Lan Li(李兰兰), Pan-Pan Yu(余盼盼), Ying Zhou(周莹),Da-Wei Guo(郭大伟), and Hong-Yi Fan(范洪义) Quantum entangled fractional Fourier transform based on the IWOP technique 2023 Chin. Phys. B 32 040302

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Quantum entangled fractional Fourier transform based on the IWOP technique

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