Deriving the Landauer Principle From the Quantum Shannon Entropy

Area of Science:

• Quantum thermodynamics
• Statistical mechanics
• Quantum information theory

Background:

• Understanding quantum states in thermal environments is crucial for quantum technologies.
• Classical thermodynamics provides a framework for energy costs but doesn't fully capture quantum effects.

Purpose of the Study:

• To derive an expression for the equilibrium probability distribution of a quantum state interacting with a noisy thermal environment.
• To establish a statistical mechanical interpretation for calculating minimum free energy costs of quantum state changes.
• To investigate the factors influencing the free energy cost of erasing or resetting a qubit.

Main Methods:

• Derivation of probability distribution separating quantum and classical uncertainty.
• Application of statistical mechanics to determine free energy costs.
• Analysis of system-bath entanglement effects on energy costs.

Main Results:

• An expression for the equilibrium probability distribution of a quantum state in a noisy thermal environment was derived.
• Minimum free energy costs for quantum state changes were determined using a statistical mechanical interpretation.
• The free energy cost to reset a qubit was found to depend on target state fidelity and environmental properties, unlike classical systems.

Conclusions:

• Quantum and classical uncertainties can be formally separated in noisy environments.
• System-bath entanglement significantly impacts the free energy costs of quantum operations.
• Resetting qubits requires careful consideration of environmental factors and state fidelity, highlighting differences from classical systems.