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Updated: Oct 3, 2025
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
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Normal product form of two-mode Wigner operator.
Rui He1, Xiangyuan Liu2,3, Xiangfei Wei2
1College of Electrical and Photoelectronic Engineering, West Anhui University, Luan, 237012, Anhui, China. heruim@wxc.edu.cn.
Scientific Reports
|February 15, 2022
Summary
We derived three representations of the two-mode Wigner operator using the integration within an ordered product (IWOP) method. This reveals the operator
Area of Science:
- Quantum optics
- Mathematical physics
Background:
- The Wigner operator is a key tool in quantum mechanics for representing quantum states.
- Understanding multi-mode Wigner operators is crucial for analyzing complex quantum systems.
Purpose of the Study:
- To derive and analyze multiple representations of the two-mode Wigner operator.
- To explore the symmetries and degrees of freedom of the two-mode Wigner operator.
- To connect the two-mode Wigner operator to entangled states.
Main Methods:
- Integration within an ordered product (IWOP) of operators.
- Derivation of SU(2) and SU(1,1) symmetric descriptions.
- Development of a polar coordinate representation.
Main Results:
- Three distinct representations of the two-mode Wigner operator were obtained.
- The two-mode Wigner operator exhibits multiple degrees of freedom.
- Changing the integral variable leads to different Wigner operator symmetries.
- A direct link between the polar coordinate form and entangled states was established.
Conclusions:
- The IWOP method provides a versatile approach to studying multi-mode Wigner operators.
- The Wigner operator's symmetry properties are dependent on the chosen representation.
- The polar coordinate representation offers new insights into quantum entanglement.
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