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

数学与统计学院

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	201-206
页数	6
期刊	Discrete Applied Mathematics
卷	232
DOI	https://doi.org/10.1016/j.dam.2017.07.008
出版状态	已出版 - 11 12月 2017

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

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AU - Hu, Dan

AU - Li, Xueliang

AU - Liu, Xiaogang

AU - Zhang, Shenggui

PY - 2017/12/11

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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

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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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