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

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

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 environm...

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Bibliographic Details
Main Authors: Laizhen Luo, Jiamei Wang, Lin Zhang, Shifang Zhang
Format: Article
Language:English
Published: MDPI AG 2016-09-01
Series:Entropy
Subjects:
Wishart matrix
random state
differential entropy
Online Access:http://www.mdpi.com/1099-4300/18/9/342
Description
Summary: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.
ISSN:1099-4300

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