The von Neumann entropy of random multipartite graphs

Dan Hu; Xueliang Li; Xiaogang Liu; Shenggui Zhang

doi:10.1016/j.dam.2017.07.008

The von Neumann entropy of random multipartite graphs

Dan Hu
, Xueliang Li
, Xiaogang Liu
, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let G be a graph with n vertices and L(G) its Laplacian matrix. Define ρ_G=[formula presented]L(G) to be the density matrix of G, where d_G denotes the sum of degrees of all vertices of G. Let λ₁,λ₂,…,λ_n be the eigenvalues of ρ_G. The von Neumann entropy of G is defined as S(G)=−∑_i=1ⁿλ_ilog₂λ_i. In this paper, we establish a lower bound and an upper bound to the von Neumann entropy for random multipartite graphs.

Original language	English
Pages (from-to)	201-206
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	232
DOIs	https://doi.org/10.1016/j.dam.2017.07.008
State	Published - 11 Dec 2017

Keywords

Density matrix
Random multipartite graphs
von Neumann entropy

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10.1016/j.dam.2017.07.008

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title = "The von Neumann entropy of random multipartite graphs",

abstract = "Let G be a graph with n vertices and L(G) its Laplacian matrix. Define ρG=[formula presented]L(G) to be the density matrix of G, where dG denotes the sum of degrees of all vertices of G. Let λ1,λ2,…,λn be the eigenvalues of ρG. The von Neumann entropy of G is defined as S(G)=−∑i=1nλilog2λi. In this paper, we establish a lower bound and an upper bound to the von Neumann entropy for random multipartite graphs.",

keywords = "Density matrix, Random multipartite graphs, von Neumann entropy",

author = "Dan Hu and Xueliang Li and Xiaogang Liu and Shenggui Zhang",

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year = "2017",

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doi = "10.1016/j.dam.2017.07.008",

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T1 - The von Neumann entropy of random multipartite graphs

AU - Hu, Dan

AU - Li, Xueliang

AU - Liu, Xiaogang

AU - Zhang, Shenggui

PY - 2017/12/11

Y1 - 2017/12/11

N2 - Let G be a graph with n vertices and L(G) its Laplacian matrix. Define ρG=[formula presented]L(G) to be the density matrix of G, where dG denotes the sum of degrees of all vertices of G. Let λ1,λ2,…,λn be the eigenvalues of ρG. The von Neumann entropy of G is defined as S(G)=−∑i=1nλilog2λi. In this paper, we establish a lower bound and an upper bound to the von Neumann entropy for random multipartite graphs.

AB - Let G be a graph with n vertices and L(G) its Laplacian matrix. Define ρG=[formula presented]L(G) to be the density matrix of G, where dG denotes the sum of degrees of all vertices of G. Let λ1,λ2,…,λn be the eigenvalues of ρG. The von Neumann entropy of G is defined as S(G)=−∑i=1nλilog2λi. In this paper, we establish a lower bound and an upper bound to the von Neumann entropy for random multipartite graphs.

KW - Density matrix

KW - Random multipartite graphs

KW - von Neumann entropy

UR - https://www.scopus.com/pages/publications/85027583211

U2 - 10.1016/j.dam.2017.07.008

DO - 10.1016/j.dam.2017.07.008

M3 - 文章

AN - SCOPUS:85027583211

SN - 0166-218X

VL - 232

SP - 201

EP - 206

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

The von Neumann entropy of random multipartite graphs

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