The von Neumann entropy and information rate for ideal quantum Gibbs ensembles

TL;DR

This paper models a quantum information source using Gibbs ensembles of free particles, linking von Neumann entropy to information rate and extending classical coding algorithms to quantum sources.

Contribution

It introduces a quantum information source model based on Gibbs ensembles and generalizes the Schumacher theorem to non-IID qubits.

Findings

Von Neumann entropy identified as the information rate.

Classical Lempel-Ziv coding extended to quantum sources.

Generalization of Schumacher theorem to non-IID qubits.

Abstract

A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical Lempel--Ziv universal coding algorithm in Grassberger's form for such a source. This generalises the Schumacher theorem to the case of non-IID qubits.