Quantum Information: What Is It All About?

TL;DR

This paper clarifies that quantum information pertains to quantum properties represented by subspaces of Hilbert space, emphasizing the importance of frameworks and the single framework rule to avoid paradoxes, and discusses the relationship with classical information theory.

Contribution

It provides a framework-based interpretation of quantum information, explaining how classical information theory extends into quantum mechanics and addressing issues with incompatible frameworks.

Findings

Quantum information is about properties represented by subspaces of Hilbert space.

The single framework rule prevents paradoxes in quantum descriptions.

Classical information theory can be applied within a single quantum framework.

Abstract

This paper answers Bell's question: What does quantum information refer to? It is about quantum properties represented by subspaces of the quantum Hilbert space, or their projectors, to which standard (Kolmogorov) probabilities can be assigned by using a projective decomposition of the identity (PDI or framework) as a quantum sample space. The single framework rule of consistent histories prevents paradoxes or contradictions. When only one framework is employed, classical (Shannon) information theory can be imported unchanged into the quantum domain. A particular case is the macroscopic world of classical physics whose quantum description needs only a single quasiclassical framework. Nontrivial issues unique to quantum information, those with no classical analog, arise when aspects of two or more incompatible frameworks are compared.