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Entropy 2016, 18(9), 342; doi:10.3390/e18090342

The Differential Entropy of the Joint Distribution of Eigenvalues of Random Density Matrices

1
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
2
School of Applied Science, Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
3
Department of Mathematics, Anhui University of Technology, Ma’Anshan 243032, China
4
Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China
5
College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350018, China
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 5 August 2016 / Revised: 11 September 2016 / Accepted: 19 September 2016 / Published: 21 September 2016
(This article belongs to the Section Information Theory)
View Full-Text   |   Download PDF [330 KB, uploaded 21 September 2016]

Abstract

We derive exactly the differential entropy of the joint distribution of eigenvalues of Wishart matrices. Based on this result, we calculate the differential entropy of the joint distribution of eigenvalues of random mixed quantum states, which is induced by taking the partial trace over the environment of Haar-distributed bipartite pure states. Then, we investigate the differential entropy of the joint distribution of diagonal entries of random mixed quantum states. Finally, we investigate the relative entropy between these two kinds of distributions. View Full-Text
Keywords: Wishart matrix; random state; differential entropy Wishart matrix; random state; differential entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Luo, L.; Wang, J.; Zhang, L.; Zhang, S. The Differential Entropy of the Joint Distribution of Eigenvalues of Random Density Matrices. Entropy 2016, 18, 342.

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