Entropy, von Neumann and the von Neumann Entropy

D�nes Petz

This paper is an introduction to the von Neumann entropy in a historic approach. Von Neumann's gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. In the analysis of his ideas we stress the role of superselection sectors and summarize von Neumann's knowledge about quantum mechanical entropy. The final part of the paper is devoted to important developments discovered long after von Neumann's work. Subadditivity and the interpretation of the von Neumann entropy as channel capacity are among those.

Glenn D. Appleby

Bijan Nikouravan

The Von Neumann entropy plays a central role in the quantum information theory and is a concave function and following the property . In this paper, we introduce a new proof for the linearity of Von Neumann entropy in the rate without using the above inequality. Here the Von Neumann entropy is concave; that is, given weights and density matrices . Roughly speaking, we will show that in the rate case, the Von Neumann entropy is linear without using Fannes inequality. https://orcid.org/0000-0003-4308-1632

Yuan Li, Paul Busch

Gong Long-Yan, Tong Pei-Qing

By using the measure of von Neumann entropy, we numerically investigate quantum entanglement of an electron moving in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. The delocalized and localized eigenstates can be distinguished by von Neumann entropy of the individual eigenstates. There are drastic decreases in von Neumann entropy of the individual eigenstates at mobility edges. In the curve of the spectrum averaged von Neumann entropy as a function of potential parameter λ, a sharp transition exists at the metal–insulator transition point λ c = 2. It is found that the von Neumann entropy is a good quantity to reflect localization and metal–insulator transition.

Mou-Hsiung Chang