On the Density Matrix of Graphs, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
Density matrix of graphs as defined -for the first time- in [S. Braunstein and et al. The laplacian of a graph as a density matrix, Annals of Combinatorics, (2006)], is obtained through dividing the Laplacian matrix by the degree sum. This matrix is also semi-positive and trace one. Therefore one may talk about the Von Neumann entropy of this matrix. In [F. Passerini, S. Severini. Quantifying complexity in networks: The Von Neumann entropy. IJATS, (2009)], authors have claimed that this quantity can be consisered as a measure of regularity. Here, using a geometric interpretation of Von Neumann entropy, expresed in [G. Mitchison, R. Jozsa, Towards a geometrical interpretation of quantum...
Cataloging briefOn the Density Matrix of Graphs, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
Density matrix of graphs as defined -for the first time- in [S. Braunstein and et al. The laplacian of a graph as a density matrix, Annals of Combinatorics, (2006)], is obtained through dividing the Laplacian matrix by the degree sum. This matrix is also semi-positive and trace one. Therefore one may talk about the Von Neumann entropy of this matrix. In [F. Passerini, S. Severini. Quantifying complexity in networks: The Von Neumann entropy. IJATS, (2009)], authors have claimed that this quantity can be consisered as a measure of regularity. Here, using a geometric interpretation of Von Neumann entropy, expresed in [G. Mitchison, R. Jozsa, Towards a geometrical interpretation of quantum...
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