Thermal Operations from Informational Equilibrium

Area of Science:

• Quantum Information Theory
• Thermodynamics
• Quantum Computation

Background:

• Thermal operations are crucial for quantum thermodynamics but lack fundamental definition.
• Existing models obscure implementation resources and fundamental principles.

Purpose of the Study:

• To identify a universal principle defining thermal operations.
• To establish a purely quantum information-theoretic characterization of thermal operations.
• To refine the hierarchy of doubly-stochastic quantum channels.

Main Methods:

• Defining thermal operations via informational equilibrium.
• Analyzing environment invariance for system inputs.
• Developing a hierarchy for doubly-stochastic quantum channels.

Main Results:

• Thermal operations are uniquely characterized by informational equilibrium.
• Energetic descriptions of equilibrium (Gibbs states) emerge from informational constraints.
• A refined hierarchy of quantum channels is established, showing strict separations.

Conclusions:

• Informational equilibrium provides a fundamental, Hamiltonian-independent definition of thermal operations.
• This framework clarifies the nature of catalytic channels and heat baths.
• The quantum hierarchy highlights limitations of classical theorems and reveals a richer quantum channel landscape.