A characterization of von Neumann entropy using functors

TL;DR

This paper extends a classical entropy characterization method to quantum systems, providing a categorical framework for understanding von Neumann entropy.

Contribution

It introduces a novel functor-based approach to characterize von Neumann entropy, building on prior classical entropy methods.

Findings

Provides a categorical characterization of von Neumann entropy

Extends classical entropy methods to quantum systems

Lays groundwork for further quantum information theory research

Abstract

Baez, Fritz, and Leinster derived a method for characterizing Shannon entropy in classical systems. In this method, they considered a functor from a certain category to the monoid of non-negative real numbers with addition as a map from measure-preserving functions to non-negative real numbers, and derived Shannon entropy by imposing several simple conditions. We propose a method for characterizing von Neumann entropy by extending their results to quantum systems.