Towards a unification of physics and information theory

TL;DR

This paper proposes a unified framework connecting quantum mechanics, thermodynamics, and information theory by extending Everett's many-worlds interpretation to include ensemble preparation and introducing directed entanglement as a central concept.

Contribution

It introduces the notion of directed entanglement to unify classical and quantum communication, thermodynamics, and information theory within a single formalism.

Findings

Proves the Holevo bound using directed entanglement.

Derives the quantum data processing inequality from entanglement properties.

Provides a simple proof of the second law of thermodynamics within the model.

Abstract

A common framework for quantum mechanics, thermodynamics and information theory is presented. It is accomplished by reinterpreting the mathematical formalism of Everett's many-worlds theory of quantum mechanics and augmenting it to include preparation according to a given ensemble. The notion of \emph{directed entanglement} is introduced through which both classical and quantum communication over quantum channels are viewed as entanglement transfer. This point is illustrated by proving the Holevo bound and quantum data processing inequality relying exclusively on the properties of directed entanglement. Within the model, quantum thermodynamic entropy is also related to directed entanglement, and a simple proof of the second law of thermodynamics is given.