Normal product form of two-mode Wigner operator

Rui He; Xiangyuan Liu; Xiangfei Wei; Congbing Wu; Gang Zhang; Min Kong

doi:10.1038/s41598-022-06124-8

Normal product form of two-mode Wigner operator

Sci Rep. 2022 Feb 14;12(1):2451. doi: 10.1038/s41598-022-06124-8.

Authors

Rui He¹, Xiangyuan Liu^{2

3}, Xiangfei Wei², Congbing Wu², Gang Zhang², Min Kong²

Affiliations

¹ College of Electrical and Photoelectronic Engineering, West Anhui University, Luan, 237012, Anhui, China. heruim@wxc.edu.cn.
² College of Electrical and Photoelectronic Engineering, West Anhui University, Luan, 237012, Anhui, China.
³ State Key Laboratory of Pulsed Power Laser Technology, School of Electronic Countermeasures, National University of Defense Technology, Hefei, 230031, Anhui, China.

Abstract

In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU(2) symmetric description, SU(1,1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.