Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics

TL;DR

This paper extends quantum hypothesis testing to a broad algebraic framework and links it with non-equilibrium quantum statistical mechanics, especially in understanding entropy flow and the arrow of time.

Contribution

It introduces a generalized mathematical framework for quantum hypothesis testing within $W^*$-algebras and connects it to non-equilibrium statistical mechanics concepts.

Findings

Established a relation between large deviation principles and hypothesis testing of the arrow of time.

Extended the theory of quantum hypothesis testing to the $W^*$-algebraic setting.

Linked entropy flow statistics with quantum hypothesis testing in non-equilibrium systems.

Abstract

We extend the mathematical theory of quantum hypothesis testing to the general $W^*$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.