Run-and-tumble exact work statistics in a lazy quantum measurement engine: stochastic information processing

TL;DR

This paper analyzes a quantum measurement engine driven by measurement backaction, revealing its stochastic work dynamics, deriving exact statistical expressions, and optimizing laziness to maximize power output.

Contribution

It introduces a lazy quantum measurement engine model, providing exact analytical work statistics and identifying optimal laziness for maximum power.

Findings

Work over cycles forms a second-order Markov process.

Exact expressions for work moments and first-passage times are derived.

Optimal laziness probability maximizes mean power output.

Abstract

We introduce a single-qubit quantum measurement engine fuelled by backaction energy input. To reduce energetic costs associated with information processing, the measurement outcomes are only used with a prescribed laziness probability in the feedback step. As a result, we show that the work extracted over consecutive cycles is a second-order Markov process, analogous to a run-and-tumble process with transient anomalous diffusion. We derive exact analytical expressions for the work finite-time moments and first-passage-time statistics. Furthermore, we find the optimal laziness probability maximizing the mean power extracted per cycle.