Natural information measures in Cox' approach for contextual probabilistic theories

TL;DR

This paper argues that von Neumann's entropy is the natural measure of information in quantum mechanics, extending Cox's probability approach to a broader non-Boolean information theory framework.

Contribution

It introduces a novel perspective linking Cox's approach to quantum entropy and generalizes the reasoning to orthomodular lattices, unveiling a general non-Boolean information theory.

Findings

von Neumann's entropy is justified as the natural quantum information measure

Generalization of Cox's probability framework to orthomodular lattices

Reveals structure of a non-Boolean information theory

Abstract

In this article we provide, from a novel perspective, arguments that support the idea that, in the wake of Cox' approach to probability theory, von Neumann's entropy should be the natural one in Quantum Mechanics. We also generalize the pertinent reasoning to more general orthomodular lattices, which reveals the structure of a general non-Boolean information theory.