A Fully Quantum Asymptotic Equipartition Property

TL;DR

This paper extends the classical asymptotic equipartition property to the quantum domain, establishing a fully quantum version with explicit convergence bounds and introducing quantum conditional entropies.

Contribution

It provides the first fully quantum asymptotic equipartition property with a convergence bound independent of side information dimension.

Findings

Proves a quantum asymptotic equipartition property.

Introduces a family of Renyi-like quantum conditional entropies.

Derives a convergence bound independent of side information dimension.

Abstract

The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtually certain to come from the typical set, each member of which is almost equally likely. In this paper, we prove a fully quantum generalization of this property, where both the output of the experiment and side information are quantum. We give an explicit bound on the convergence, which is independent of the dimensionality of the side information. This naturally leads to a family of Renyi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.