Finite-Time Quantum Landauer Principle and Quantum Coherence

TL;DR

This paper explores the finite-time heat dissipation limits in quantum information erasure, highlighting how quantum coherence increases heat costs, with theoretical bounds and an optimal control protocol demonstrated on a single-qubit system.

Contribution

It derives bounds linking quantum coherence to heat dissipation during finite-time erasure and presents an optimal control protocol for minimizing heat costs.

Findings

Heat dissipation is bounded by Landauer's principle plus a time-dependent correction.

Quantum coherence in the energy basis increases heat costs during erasure.

An optimal control protocol reduces heat dissipation in a single-qubit system.

Abstract

The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this study, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower-bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.