The Quantum Relative Entropy as a Rate Function and Information Criteria

TL;DR

This paper establishes the quantum relative entropy as a rate function within large deviation principles and introduces quantum information criteria, assessing their accuracy based on foundational theorems.

Contribution

It demonstrates the quantum relative entropy's role as a rate function and develops quantum information criteria with accuracy estimates, extending classical large deviation theory.

Findings

Quantum relative entropy is a valid rate function in large deviation principles.

Quantum information criteria can be effectively estimated for quantum states.

Most results rely on the Hiai-Ohya-Tsukada theorem.

Abstract

We prove that the quantum relative entropy is a rate function in large deviation principle. Next, we define information criteria for quantum states and estimate the accuracy of the use of them. Most of the results in this paper are essentially based on Hiai-Ohya-Tsukada theorem.