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Chinese Physics Letters

Measurement-Conditioned Coherent Control: Driving-Speed and Measurement-Basis Optimization in Quantum Heat Engines

Yerong Li, Yingying Hong, Weiwei Zhang, Jianhui Wang

Published Mar 18, 2026• 3 citations
Publisher

Abstract

Abstract We theoretically propose a cyclic quantum engine in which a single-qubit working medium undergoes finite-time unitary strokes with adjustable durations, followed by a projective measurement and an outcome-dependent coherent pulse ( π or π /2 rotation). The protocol separates two independent control handles: the unitary driving speed τ dr , which governs nonadiabatic transitions and phase accumulation, and the measurement parameter θ , which sets the outcome probabilities and the magnitude of measurement-induced energy injection. Feedback functions solely through pulses without altering the stroke time. Including the measurement and erasure costs, we show that the coordinated tuning of τ dr and θ yields substantial and robust gains in terms of power and efficiency.

DOI
10.1088/0256-307x/43/4/040005

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Abstract We theoretically propose a cyclic quantum engine in which a single-qubit working medium undergoes finite-time unitary strokes with adjustable durations, followed by a projective measurement and an outcome-dependent coherent pulse ( π or π /2 rotation). The protocol separates two independent control handles: the unitary driving speed τ dr , which governs nonadiabatic transitions and phase accumulation, and the measurement parameter θ , which sets the outcome probabilities and the magnitude of measurement-induced energy injection. Feedback functions solely through pulses without altering the stroke time. Including the measurement and erasure costs, we show that the coordinated tuning of τ dr and θ yields substantial and robust gains in terms of power and efficiency.
Harnessing finite-time nonadiabatic transitions that are conventionally associated with quantum inner friction for useful work extraction remains an open experimental challenge. Here we address this issue by introducing and experimentally realizing an innovative measurement-feedback quantum information engine model in the trapped 40Ca+ ion system, in which the projective measurement replaces the hot reservoir as a nonthermal energy source and the feedback control conditionally steers the system through either unitary compression-expansion strokes or thermalization. We experimentally show that the repeated feedback cycle converges to a stable operating regime with a resolved energetic balance, and, by controlling the measurement angle and stroke duration, measurement-induced coherence and the finite-time nonadiabatic contribution can enhance work extraction and raise the efficiency above the corresponding Otto benchmark. The experimental results further show that, over finite ranges of stroke durations, the efficiency and intrinsic cycle power can increase simultaneously. Our experiment establishes a route toward information-to-work quantum engines that convert finite-time irreversibility into performance-enhancing resources.
Finite-time quantum heat engines (QHEs) typically extract less work than their quasistatic counterparts because fast driving generates coherences and non-adiabatic transitions during the work strokes, a phenomenon commonly referred to as quantum friction. Quantum lubrication denotes a broad class of strategies that use auxiliary systems or controls to mitigate this loss. In this work, we introduce a lubrication protocol based on the quantum Zeno dynamics (QZD). By coupling the working medium to an auxiliary lubricant system and frequently monitoring the lubricant, we confine the joint evolution to a Zeno subspace and obtain an effective shortcut to adiabaticity during the work strokes of a QHE running an Otto cycle. In the ideal Zeno limit, the protocol reproduces the transitionless dynamics required to preserve populations in the instantaneous energy basis and recover the Otto efficiency at finite stroke duration. We also analyze several implementation-dependent thermodynamic costs, including switching, driving, monitoring, and imperfect thermalization, in order to assess how these costs constrain the practical gains in efficiency and power. Our results identify QZD as a conceptually distinct route to quantum lubrication and highlight quantum heat engines as a useful setting in which to study the interplay between strong coupling, measurement, and quantum thermodynamic control.
An analytical study of a feedback-driven quantum engine based on a two-level system is presented. This engine is similar to a quantum Otto engine but substitutes the quantum isochoric process with a feedback-driven operation based on a measured observable $A(\ensuremath{\theta})$, whose eigenstates are coherent superpositions of energy eigenstates. Projective measurements control the feedback operations, while work extraction or heat absorption occurs during driven operations. We derive the general time-dependent efficiency, power, and power fluctuations. Quantum coherence is examined through three mechanisms: (i) coherence associated with $\ensuremath{\theta}\ensuremath{\ne}0$, (ii) residual coherence after incomplete thermalization, and (iii) coherence generated by the interaction between the system and a coherent laser pulse on resonance. We investigate how the parameter $\ensuremath{\theta}$, quantum coherence, and timing of unitary and feedback-driven strokes influence engine performance. We demonstrate that quantum coherence can significantly enhance power output and efficiency while reducing fluctuations through optimal cycle parameter adjustments.
Abstract In feedback controls, measurement is an essential step in designing protocols according to outcomes. For quantum mechanical systems, measurement has another effect; to supply energy to the measured system. We verify that in feedback-controlled quantum engines, measurement plays a dual role; not only as an auxiliary to perform feedback control but also as an energy supply to drive the engines. We consider a specific engine cycle exploiting feedback control followed by projective measurement and show that the maximum bound of the extractable work is set by both the efficacy of the feedback control and the energy change caused by projective measurement. We take a concrete example of an engine using an immobile spin-1/2 particle as a working substance and suggest two possible scenarios for work extraction.
Thermodynamic Performance of a Measurement-Driven Quantum Engine with a Two-Parameter (p,q)(p,q)(p,q)-Deformed Harmonic Oscillator
We address a measurement-driven, single-bath quantum engine that generates usable work using quantum measurement backaction. The working medium is a two-parameter (p,q)(p,q)(p,q)-deformed harmonic oscillator, whose nonlinear spectrum modifies the energy gaps sampled by a nonselective Gaussian measurement and the work exchanged during quasistatic adiabatic strokes. The cycle starts from a Gibbs state and consists of an adiabatic change of (ω,p,q)(ω,p,q)(ω,p,q), measurement of the final effective position quadrature, a reverse adiabatic stroke, and thermalization with the original bath. Using a consistent first-law convention, we derive the measurement heat, adiabatic work contributions, thermalization heat, and reduced working-medium efficiency. We also express the measurement stroke via a transition matrix and identify passivity/unitality conditions that ensure nonnegative measurement heat. Numerical scans show that, within the finite-basis, spectral-ordering, and engine-operation checks used in this work, deformation can enhance measurement-induced energy input and extracted work relative to the undeformed oscillator. The physical engine regime is selected by $\QM>0$, $\Wcyc<0$, $\QT<0$, and 0<η<10<η<10<η<1. The reported efficiency is reduced and excludes measurement-apparatus costs.
We present a measurement-based quantum thermal machine that extracts work from the back-action of generalized quantum measurements whose working medium is a coupled two-level quantum system. Specifically, we derive universal optimization criteria for a three-stroke measurement-based engine cycle with coupled two-level system of Ising-like interaction as a working medium. Furthermore, we present two numerical algorithms to optimize the engine work extraction and enhance its performance. Our numerical results demonstrate: (i) efficiency peaks in the projective-measurement limit; (ii) symmetry breaking (detuning or weak coupling) enlarges the exploitable energy gap; and (iii) performance remains robust (>50%>50\%>50% of optimum) under ∼ ⁣10∘\sim\!10^\circ∼10∘ feedback-pulse errors. The framework is platform-agnostic and directly implementable with current superconducting, trapped-ion, or NMR technologies, providing a concrete route to scalable, measurement-powered quantum thermal machines.