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arXiv:2404.17431

Quantum Information Engines: Assessing Time, Cost and Performance Criteria

Henning Kirchberg, Abraham Nitzan

Published Apr 26, 2024• 0 citations
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Abstract

In this study, we investigate the crucial role of measurement time ($t_m$), information gain and energy consumption in information engines (IEs) utilizing a von-Neumann measurement model. These important measurement parameters allow us to analyze the efficiency and power output of these devices. As the measurement time increases, the information gain and subsequently the extracted work also increase. However, there is a corresponding increase in the energetic cost. The efficiency of converting information into free energy diminishes as $t_m$ approaches both 0 and infinity, peaking at intermediate values of $t_m$. The power output (work extracted per times) also reaches a maximum at specific operational time regimes. By considering the product of efficiency and power as a performance metric, we can identify the optimal operating conditions for the IE.

DOI
10.48550/arxiv.2404.17431

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In this study, we investigate the crucial role of measurement time (tmt_mtm​), information gain and energy consumption in information engines (IEs) utilizing a von-Neumann measurement model. These important measurement parameters allow us to analyze the efficiency and power output of these devices. As the measurement time increases, the information gain and subsequently the extracted work also increase. However, there is a corresponding increase in the energetic cost. The efficiency of converting information into free energy diminishes as tmt_mtm​ approaches both 0 and infinity, peaking at intermediate values of tmt_mtm​. The power output (work extracted per times) also reaches a maximum at specific operational time regimes. By considering the product of efficiency and power as a performance metric, we can identify the optimal operating conditions for the IE.
Information engines, sometimes referred to as Maxwell Demon engines, utilize information obtained through measurement to control the conversion of energy into useful work. Discussions around such devices often assume the measurement step to be instantaneous, assessing its cost by Landauer's information erasure within the measurement device. While this simplified perspective is sufficient for classical feedback-controlled engines, for nanoengines that often operate in the quantum realm, the overall performance may be significantly affected by the measurement duration (which may be comparable to the engine's cycle time) and cost (energy needed to create the system-meter correlation). In this study, we employ a generalized von Neumann measurement model to highlight that obtaining a finite amount of information requires a finite measurement time and incurs an energetic cost. We investigate the crucial role of these factors in determining the engine's performance, particularly in terms of efficiency and power output. Furthermore, for the information engine model under consideration, we establish a precise relationship between the acquired information in the measurement process and the maximum energy extractable through the measurement. We also discuss ways to extend our considerations using these concepts, such as in measurement-enhanced photochemical reactions.
Abstract Information engines harness measurement and feedback to convert energy into useful work. In this study, we investigate the fundamental trade-offs between ergotropic output power, thermodynamic efficiency and information-to-work conversion efficiency in such engines, explicitly accounting for the finite time required for measurement. As a model engine, we consider a two-level quantum system from which work is extracted via a temporarily coupled quantum harmonic oscillator that serves as the measurement device. This quantum device is subsequently read out by a classical apparatus. We compute trade-offs for the performance of the information engine using Pareto optimisation, which has recently been successfully used to optimise performance in engineering and biological physics. Our results offer design principles for future experimental implementations of information engines, such as in nano-mechanical systems and circuit quantum electrodynamics (QED) platforms.
Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.
We study a finite-time quantum information engine in which a two-level system is measured by a quantum harmonic oscillator acting as a meter and where useful work is extracted conditionally on the measurement outcome. Using multi-objective optimisation, we find a Pareto-optimal trade-off between extractable work and its fluctuations and show that reducing fluctuations entails higher thermodynamic costs: greater information consumption, more engine cycles, longer operation time, and reduced average work output. In the limit of a highly accurate meter, we obtain the work distribution, its moments, and the Pareto front analytically. In this regime, the work statistics of the engine reduce to those of a qubit in contact with a single thermal bath. We further analyse the associated information flows by examining the mutual information and Fisher information, and show that the Pareto-optimal engine designs lie very close to local maxima of the latter with respect to the operation time of the device. Our results provide a compact description of the trade-offs between work, its fluctuations, and thermodynamic costs in quantum information engines.
Efficiency and power are two central measures of the performance of thermal machines. We here study the power-efficiency-stability trade-off in a finite-time quantum Carnot information engine, in which an information reservoir replaces the usual cold bath of a quantum Carnot engine. We analytically evaluate mean and variance of the work output, and demonstrate that maximum efficiency can be reached at both finite work output and finite work output fluctuations. We additionally show that the relative work output fluctuations may be smaller than those of the corresponding Carnot heat engine. This result implies that the finite-time quantum Carnot information engine can be more stable than the quantum Carnot heat engine, an important property for practical applications.
Considering a general microscopic model for a quantum measuring apparatus comprising a quantum probe coupled to a thermal bath, we analyze the energetic resources necessary for the realization of a quantum measurement, which includes the creation of system-apparatus correlations, the irreversible transition to a statistical mixture of definite outcomes, and the apparatus resetting. Crucially, we do not resort to another quantum measurement to capture the emergence of objective measurement results, but rather exploit the properties of the thermal bath which redundantly records the measurement result in its degrees of freedom, naturally implementing the paradigm of quantum Darwinism. In practice, this model allows us to perform a quantitative thermodynamic analysis of the measurement process. From the expression of the second law, we show how the minimal required work depends on the energy variation of the system being measured plus information-theoretic quantities characterizing the performance of the measurement – efficiency and completeness. Additionally, we show that it is possible to perform a thermodynamically reversible measurement, thus reaching the minimal work expenditure, and provide the corresponding protocol. Finally, for finite-time measurement protocols, we illustrate the increasing work cost induced by rising entropy production inherent in finite-time thermodynamic processes. This highlights an emerging trade-off between velocity of the measurement and work cost, on top of a trade-off between efficiency of the measurement and work cost. We apply those findings to bring new insights in the thermodynamic balance of the measurement-powered quantum engines.