Effect of quantum coherence on Landauer's principle

TL;DR

This paper investigates how quantum coherence influences Landauer's principle, comparing entropic and thermodynamic bounds under various initial states and dynamics, revealing conditions where each bound is tighter and highlighting the energetic cost of creating system-reservoir correlations.

Contribution

It extends the comparison of Landauer's bounds to include quantum coherence effects, analyzing their dependence on initial states and dynamics, and identifies conditions where each bound is tighter.

Findings

Entropic bound is tighter for mixed initial states.

Thermodynamic bound is tighter for high-purity initial states.

Quantum coherence affects the relation between bounds and energy dissipation.

Abstract

Quantum Landauer's principle provides a fundamental lower bound for energy dissipation occurred with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound~(entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy~(thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system--reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system--reservoir correlation, which may cause an additional source of energetic cost for the erasure.