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arXiv:2607.14973

Pareto-optimal work extraction and the thermodynamic cost of precision in quantum information engines

Jonas Berx, Ted Olander, Henning Kirchberg

quant-phSubmitted Jul 16, 2026• Announced Jul 17, 2026• 0 citations
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Abstract

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.

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arXiv:2003.05788•Quantum•Dec 23, 2020•25 citations
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.
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.
Measurement-based quantum heat engines have attracted significant interest as alternatives to conventional thermal engines, as they replace the hot thermal reservoir with quantum measurements, thereby offering greater controllability and simpler implementation. Motivated by these advantages, we investigate a measurement-driven quantum Otto engine with a qubit working substance and study the optimal work extractable from such engines, including whether their performance can surpass that of conventional quantum Otto cycles. We analyze the engine in both the infinite-time (adiabatic) and finite-time (non-adiabatic) regimes, considering two distinct implementations obtained through optimization over all projection-valued measurements (PVMs) and over all two-outcome positive operator-valued measurements (POVMs). We show that measurement-based engines can outperform conventional quantum Otto engines within specific parameter regimes and that POVM-based engines can yield higher optimal work extraction than PVM-based ones. Furthermore, by incorporating the thermodynamic cost associated with resetting the auxiliary system required for POVM implementation, we demonstrate that the resulting net work output can still exceed that of PVM-based engines under suitable conditions on the spectral gaps and cold bath temperature. We also identify regimes in which non-adiabatic implementations can yield higher work output and efficiency than their adiabatic counterparts. Our study provides operational guidelines for designing improved measurement-driven quantum Otto engines.
A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on Reinforcement Learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal trade-offs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.
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.
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.