Thermal operations from informational equilibrium

TL;DR

This paper characterizes thermal operations as channels that preserve equilibrium via a unique quantum dilation, and explores catalytic channels as an idealized model of heat bath behavior with implications for Gibbs-preserving maps and quantum circuits.

Contribution

It introduces a quantum information theoretic characterization of thermal operations and analyzes catalytic channels as an idealization of heat bath interactions.

Findings

Thermal operations admit a dilation into a unitary process leaving the environment invariant.

Catalytic channels form a hierarchy of Gibbs-preserving maps for degenerate Hamiltonians.

Catalytic channels are related to dual unitary quantum circuits.

Abstract

Thermal operations are quantum channels that have taken a prominent role in deriving fundamental thermodynamic limitations in quantum systems. We show that these channels are uniquely characterized by a purely quantum information theoretic property: They admit a dilation into a unitary process that leaves the environment invariant when applied to the equilibrium state. In other words, they are the only channels that preserve equilibrium between system and environment. Extending this perspective, we explore an information theoretic idealization of heat bath behavior, by considering channels where the environment remains locally invariant for every initial state of the system. These are known as catalytic channels. We show that catalytic channels provide a refined hierarchy of Gibbs-preserving maps for fully-degenerate Hamiltonians, and are closely related to dual unitary quantum circuits.