The Quantum Theil Index: Characterizing Graph Centralization using von Neumann Entropy

Calculating Different Topological Indices of Von Neumann Regular Graph of Z_(p^α )

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

Quantifying Disorder in Networks: The von Neumann Entropy

The von Neumann entropy (or equivalently quantum entropy) was defined by von Neumann (1955) in his fundational work in quantum mechanics. Nowadays the von Neumann entropy is an important tool in quantum information theory (see Nielsen and Chuang (2001); Ohya and Petz (1993)). In the present work we first associate a graph to a quantum state, injectively. Then, we study the von Neumann entropy o...

Symmetric Laplacians, Quantum Density Matrices and their Von-Neumann Entropy

We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian’s Von Neumann entropy as a measure of bipartite entanglement present betw...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

The smooth entropy formalism for von Neumann algebras

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional minand max-entropy we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-di...