Von Neumann Entropy - Uses

Uses

The von Neumann entropy is being extensively used in different forms (conditional entropies, relative entropies, etc.) in the framework of quantum information theory. Entanglement measures are based upon some quantity directly related to the von Neumann entropy. However, there have appeared in the literature several papers dealing with the possible inadequacy of the Shannon information measure, and consequently of the von Neumann entropy as an appropriate quantum generalization of Shannon entropy. The main argument is that in classical measurement the Shannon information measure is a natural measure of our ignorance about the properties of a system, whose existence is independent of measurement.

Conversely, quantum measurement cannot be claimed to reveal the properties of a system that existed before the measurement was made. This controversy has encouraged some authors to introduce the non-additivity property of Tsallis entropy (a generalization of the standard Boltzmann–Gibbs entropy) as the main reason for recovering a true quantal information measure in the quantum context, claiming that non-local correlations ought to be described because of the particularity of Tsallis entropy.