Entropy, von Neumann and the von Neumann entropy

TL;DR

This paper provides a historical overview of von Neumann entropy, revisiting von Neumann's original ideas and exploring subsequent developments like subadditivity and quantum channel capacity interpretations.

Contribution

It offers a comprehensive historical and conceptual analysis of von Neumann entropy, highlighting its evolution and significance in quantum information theory.

Findings

Revisits von Neumann's original thought experiment

Summarizes key developments like subadditivity

Discusses von Neumann entropy as channel capacity

Abstract

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.