Note on von Neumann and Rényi entropies of a Graph

2016/09/01 by Dairyko, Michael, Hogben, Leslie, Lin, Jephian C. -H. +4
#05C50 #81P45 #94A17 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1609.00420

Abstract

We conjecture that all connected graphs of order n have von Neumann entropy at least as great as the star K_1,n-1 and prove this for almost all graphs of order n. We show that connected graphs of order n have Rényi 2-entropy at least as great as K_1,n-1 and for α>1, K_n maximizes Rényi α-entropy over graphs of order n. We show that adding an edge to a graph can lower its von Neumann entropy.

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