Effect of Quantum Coherence on Landauer's Principle

Area of Science:

• Quantum Information Theory
• Thermodynamics
• Statistical Mechanics

Background:

• Landauer's principle establishes a fundamental limit on energy dissipation during information erasure.
• Two bounds exist: the entropic bound (related to entropy reduction) and the thermodynamic bound (related to thermal fluctuations).
• Previous comparative studies were limited to systems with decoupled population and coherence dynamics.

Purpose of the Study:

• To compare the entropic and thermodynamic bounds for information erasure.
• To investigate the influence of quantum coherence, induced by tilted system-reservoir interactions, on these bounds.
• To analyze the dependence of bound tightness on the initial state's purity and coherence.

Main Methods:

• Theoretical analysis of quantum information erasure in a system with tilted system-reservoir interaction.
• Examination of the time-evolution of density matrix elements (diagonal and off-diagonal).
• Comparative study of entropic and thermodynamic bounds based on initial state properties.

Main Results:

• The entropic bound is tighter for mixed initial states, while the thermodynamic bound is tighter for pure initial states.
• This holds true even when quantum coherence is present due to system-reservoir interactions.
• An exception occurs in phase relaxation dynamics where bounds coincide for zero initial coherence.

Conclusions:

• The relative tightness of entropic and thermodynamic bounds depends on initial state purity and coherence.
• Quantum coherence induced by system-reservoir interactions does not alter this general trend.
• Information erasure can incur additional energy costs due to system-reservoir correlations.