Energetics of Feedback: Application to Memory Erasure

TL;DR

This paper investigates the energetics of feedback-based memory erasure, demonstrating how measurement imperfections and mutual information influence work costs, with experimental validation using optical memory protocols.

Contribution

It provides a quantitative analysis of feedback erasure energetics considering real-world imperfections and experimentally validates the theoretical findings.

Findings

Mutual information accounts for the work deficit below Landauer's limit.

Measurement imperfections increase the work required for erasure.

Experimental optical memory protocol confirms theoretical predictions.

Abstract

Landauer's erasure principle states that any irreversible erasure protocol of a single bit memory needs work of at least $k_B T ln2.$ Recent proof of concept experiments has demonstrated that the erasure protocols with work close to the Landauer limit can be devised. Under feedback, where the state of the bit can be measured, the work needed for bit erasure can be lower than $k_B T ln2.$ In this article, we analyze the energetics of feedback enabled erasure, while incorporating the imperfections of experimentally realized memory and bit erasure protocols that admit failure probabilities. We delineate the role of uncertainty in measurements and its effects on the work and entropy changes for a feedback-based erasure. We quantitatively demonstrate that the deficit between the Landauer limit and the minimum average work needed in a feedback-based erasure is accounted for by the mutual information between the measurement and the state of the memory, while incorporating the imperfections inherent in any realization. We experimentally demonstrate analysis results on a memory and erasure protocol realized using optical fields.