Thermodynamic Implementations of Quantum Processes

Area of Science:

• Quantum Thermodynamics
• Information Theory
• Statistical Mechanics

Background:

• Thermodynamics of small systems advances quantum process characterization for fixed inputs.
• Existing methods focus on specific input states, limiting universal applicability.

Purpose of the Study:

• To develop optimal universal implementations of quantum processes accurate for any input state.
• To determine the fundamental thermodynamic cost of such universal implementations.

Main Methods:

• Extending thermodynamic characterization to universal implementations.
• Defining and analyzing the 'thermodynamic capacity' of a quantum process.
• Utilizing convex-split methods and exploring quantum typicality.

Main Results:

• Optimal universal implementations are accurate for all input states after repeated processes.
• The work cost rate is governed by the process's thermodynamic capacity.
• Thermodynamic capacity is a single-letter, additive quantity defined by relative entropy differences.

Conclusions:

• The findings establish a thermodynamic analogue to the reverse Shannon theorem for quantum channels.
• Introduces a novel concept of quantum typicality with practical thermodynamic applications.
• Provides a theoretical framework for efficient and accurate quantum information processing.