Eur. Phys. J. B (2014) 87: 193
https://doi.org/10.1140/epjb/e2014-50330-y

Regular Article

The relations among Shannon information entropy, quantum discord, concurrence and localization properties of one-dimensional single-electron wave functions

¹ Department of Applied Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, P.R. China
² Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, P.R. China

^a e-mail: lygong@njupt.edu.cn

Received: 23 May 2014
Received in final form: 2 July 2014
Published online: 1 September 2014

Abstract

Shannon information entropy (SE), concurrence (CC), quantum discord (QD) and localization properties for various one-dimensional one-electron wave functions are intensively studied, respectively. They include Gaussian functions, power-law functions, and functions in the Anderson model and the Harper ones. For all these wave functions, we find that SE, CC and QD increase as the localization length of a wave function increases, respectively. There are linear or quadratic relationships between two of them. Therefore, we can confirm for the analyzed models that SE, CC and QD are statistically equivalent quantities to reflect the localization properties of wave functions though they are different measures of quantum information.