Quantifying Disorder in Networks: The von Neumann Entropy
نویسندگان
چکیده
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 of the state itself. Since the information contained in the state is nothing more but the information contained in the graph, with an easy abuse of language, we can say that we study the von Neumann entropy of the graph. Our purpose is to get a feeling about the properties of a network that are readable through the Neumann entropy. During our discussion, we will guess that the properties highlighted by the entropy are related, even if not in a clear way, to the amount of symmetry in a graph. Entropy is axiomatically connected to the amount of disorder. Somehow, disorder and complexity may be seen ABSTRACT
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