Ye, L.; Huang, Y.; Osborn, J.C.; Wei, L. Square Root Statistics of Density Matrices and Their Applications. Entropy 2024, 26, 68, doi:10.3390/e26010068.
Ye, L.; Huang, Y.; Osborn, J.C.; Wei, L. Square Root Statistics of Density Matrices and Their Applications. Entropy 2024, 26, 68, doi:10.3390/e26010068.
Ye, L.; Huang, Y.; Osborn, J.C.; Wei, L. Square Root Statistics of Density Matrices and Their Applications. Entropy 2024, 26, 68, doi:10.3390/e26010068.
Ye, L.; Huang, Y.; Osborn, J.C.; Wei, L. Square Root Statistics of Density Matrices and Their Applications. Entropy 2024, 26, 68, doi:10.3390/e26010068.
Abstract
To estimate the degree of quantum entanglement, it is important to understand
the statistical behavior of functions of spectrum of density matrices such as von
Neumann entropy, quantum purity, and entanglement capacity. These entangle-
ment metrics over different generic state ensembles have been studied intensively
in the literature. As an alternative metric, in this work we study sum of square
root spectrum of density matrices, which is relevant to negativity and fidelity in
quantum information processing. In particular, we derive the exact mean and vari-
ance of sum of square root spectrum over the Bures-Hall generic state ensemble
extending known results obtained recently over the Hilbert-Schmidt ensemble.
Keywords
quantum entanglement, negativity, fidelity, Bures-Hall ensemble, random matrix theory
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
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.
