Universal Characterization of Quantum Vacuum Measurement Engines

TL;DR

The paper develops a universal geometric framework for quantum vacuum measurement engines by introducing the quantum vacuum bending function $\Delta(\lambda)$, which encodes how the ground-state energy lowers as the coupling is turned on. It shows that all thermodynamic observables, including work, quantum heat, and efficiency, depend only on $\Delta(\lambda)$ and its derivatives, while work fluctuations are set by the curvature $\Delta''(\lambda)$ weighted by an effective energy $\bar{e}(\lambda)$ and bounded by a quantum Fisher information–based uncertainty relation. A nonperturbative, information-geometry perspective is established, linking fluctuations to both the geometry of the ground-state landscape and to quantum metrological bounds. The framework is validated across diverse models—qubits and harmonic oscillators, including many-body systems like the transverse-field Ising model and random-coupling qubit networks—demonstrating that the QVBF geometry governs engine performance irrespective of microscopic details, and offering design principles for efficient, measurement-powered quantum machines.

Abstract

Quantum measurements can inject energy into quantum systems, enabling engines whose operation is powered entirely by measurements. We develop a general theory of quantum vacuum measurement engines by introducing the quantum vacuum bending function (QVBF), a quantity that characterizes the lowering of the ground-state energy due to interactions. We show that all thermodynamic observables, including work and efficiency, are governed solely by the shape of the ground-state energy landscape encoded in the QVBF, regardless of microscopic details. We further demonstrate that work fluctuations are defined by the curvature of QVBF modulated by a model-dependent quantity, and are constrained by a generalized quantum fluctuation relation that involves the interplay between quantum Fisher information and the ground-state energy landscape. Exactly solvable models and numerical simulations of single and many-body systems confirm the theory and illustrate how the QVBF alone determines the performance of quantum vacuum measurement engines.

Figures (6)

• Figure 1: Schematic of a quantum vacuum measurement engine in a many-body setting. Switching on the parameter $\lambda$ corresponds to activating the coupling between spins. The labels above each square indicate whether the coupling in the Hamiltonian is on ($H(\lambda)$) or off ($H(0)$), followed by the quantum state of the system at that stage of the cycle. The protocol consists of six steps: (i) initialization, (ii) measurement, (iii) rapid switching off of the coupling, (iv) work extraction, (v) rapid switching on of the coupling, and (vi) relaxation.
• Figure 2: Results for a 10-qubit quantum vacuum measurement engine with randomly chosen couplings, computed using only the quantum vacuum bending function $\Delta(\lambda)$. Top panel: the $\Delta(\lambda)$ and its first and second derivatives. Bottom panel: work $W$ and its fluctuations $\sigma$ with the corresponding values given on the left y-axis, efficiency $\eta$ with its corresponding values given on the right y-axis. $\Delta(\lambda)$, its derivatives, $W(\lambda)$, and $\sigma(\lambda)$ are plotted in units of the qubit energy gap $\varepsilon_q$. The coupling values used to generate the data are provided in the Supplementary Material SM.
• Figure 3: Comparison of five types of measurement engines described in Tab. \ref{['tab:descriptions']}: single qubit, coupled qubits, single harmonic oscillator, coupled harmonic oscillators, and a $10$-qubit engine with randomly selected couplings. The red curves correspond to the $10$-qubit results shown in Fig. \ref{['fig:multiple_engines']}. Panel (a) shows the entanglement gap $\Delta(\lambda)$; the inset displays the same quantity over a smaller range of $\lambda$. Panel (b) presents the extracted work, with the inset restricted to qubit-based engines. Panel (c) shows the work fluctuations, and panel (d) displays the engine efficiency. The energy unit $\omega$ denotes the qubit energy gap for qubit-based engines and the level spacing for oscillator-based engines.
• Figure 4: Results describing $N=2$ coupled qubits. (a) QVBF and its derivatives. (b) Work (solid lines) and fluctuations (dotted lines) evaluated from $\sqrt{\sigma^2}$. The grey dashed line corresponds to the asymptotic limit given in Eq. \ref{['eq:W_2qubits_asymptote']} (c) Quantum heat. (d) Efficiency. Panels (a), (b) and (c) are plotted in the units of qubit energy gap $\varepsilon_q$.
• Figure 5: Results for $\Delta, W, \eta$ as a function of $\lambda$, all computed with knowledge of $\Delta(\lambda)$ only.