Some definitions of quantum entropy based on Wigner function

LIN Bing-sheng, HENG Tai-hua

doi:10.16854 /j.cnki.1000-0712.180498

College Physics >

2019 , Vol. 38 >Issue 3: 1 - 3

DOI: https://doi.org/10.16854 /j.cnki.1000-0712.180498

Some definitions of quantum entropy based on Wigner function

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1.School of Mathematics，South China University of Technology，Guangzhou，Guangdong 510641，China; 2.School of Physics and Material Science，Anhui University，Hefei，Anhui 230601，China

Received date: 2018-09-07

Revised date: 2018-11-09

Online published: 2019-04-25

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Abstract

Some quantum entropy，such as von Neumann entropy，linear entropy，Rényi entropy，Tsallis entropy，

and several different definitions of them based on Wigner functions in phase space，are introduced respectively.

Through some theoretical deductions and numerical calculations，the definitions of quantum entropy in phase

space using the absolute value of Wigner function in the literatures are proved to be inappropriate. The quantum entropy

defined in this paper by the Moyal star product of Wigner function is consistent with that defined by density

　　matrices.

Key words： Wigner function; von Neumann entropy; Tsallis entropy; Rényi entropy; linear entropy

Cite this article

LIN Bing-sheng, HENG Tai-hua . Some definitions of quantum entropy based on Wigner function[J]. College Physics, 2019 , 38(3) : 1 -3 . DOI: 10.16854 /j.cnki.1000-0712.180498

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