Deriving the Landauer Principle From the Quantum Shannon Entropy

TL;DR

This paper derives a quantum version of the Landauer principle, showing that the minimum energy cost to erase a qubit depends on quantum entanglement and environmental factors, extending classical thermodynamics to quantum systems.

Contribution

It provides a formal derivation of the Landauer principle for quantum systems, incorporating quantum and classical uncertainties and system-bath entanglement effects.

Findings

Quantum free energy cost depends on target state fidelity.

Environmental properties influence erasure energy costs.

Quantum entanglement affects thermodynamic limits.

Abstract

We derive an expression for the equilibrium probability distribution of a quantum state in contact with a noisy thermal environment that formally separates contributions from quantum and classical forms of probabilistic uncertainty. A statistical mechanical interpretation of this probability distribution enables us to derive an expression for the minimum free energy costs for arbitrary (reversible or irreversible) quantum state changes. Based on this derivation, we demonstrate that - in contrast to classical systems - the free energy required to erase or reset a qubit depends sensitively on both the fidelity of the target state and on the physical properties of the environment, such as the number of quantum bath states, due primarily to the entropic effects of system-bath entanglement.