Correlations in a quantum switch-based heat engine with measurements: A proof-of-principle demonstration

TL;DR

The paper addresses how indefinite causal order, realized by the quantum SWITCH, affects a measurement-driven heat engine and how initial correlations between the working medium and controller modify performance. It models a qubit with $H = -\varepsilon Z$, driven by two generalized measurements whose order is put in superposition, and derives how work $\mathcal{W}_{ext}$ and efficiency $\eta$ depend on measurement strengths and correlations, including a Landauer erasure cost for post-selection. A key result is that entanglement between the working medium and controller enables SCO to generate coherence in the working medium, yielding higher extractable work and efficiency than in uncorrelated or merely separable cases; separable correlations also broaden the SCO-active region, especially at high temperature. The authors provide a proof-of-principle demonstration on IBM Quantum Experience, implementing SCO between two measurement channels and experimentally validating coherence-assisted enhancements, highlighting the thermodynamic value of quantum correlations and indefinite causal structure for quantum devices.

Abstract

Allowing the order of quantum operations to exist in superposition is known to open new routes for thermodynamic tasks. We investigate a quantum heat engine where energy exchanges are driven by generalized measurements, and the sequence of these operations is coherently controlled in a superposition of causal orders. Our analysis explores how initial correlations between the working medium and the controller affect the engine's performance. Considering uncorrelated, classically correlated, and entangled initial states, we show that entanglement enables the superposed causal order to generate coherence in the working medium, thereby enhancing work extraction and efficiency beyond the separable and uncorrelated cases. Finally, we present a proof-of-principle simulation on the IBM Quantum Experience platform, realizing a quantum switch of two measurement channels with tunable strengths and experimentally confirming the predicted efficiency enhancement enabled by correlation-assisted superposed causal order.

Figures (16)

• Figure 1: Heat engine protocol powered by a quantum SWITCH on two measurement channels.(0) The protocol starts with the medium $\mathbf{Q}$ and controller $\mathbf{C}$ sharing thermal correlations, where $\mathbf{Q}$ is locally in a thermal state as given by \ref{['eq:localThermalState']}. (0-1) In the first stroke, generalized measurements are performed on $\mathbf{Q}$ via measurement apparata $\mathbf{A}$ and $\mathbf{A'}$, with their causal order controlled by the quantum SWITCH. (1-2) To enable work extraction in the second stroke, a generalized measurement is applied to $\mathbf{Q}$ using apparatus $\mathbf{B}$, conditioned on the outcome of a prior measurement of the controller $\mathbf{C}$ of the quantum SWITCH. (2-3) In the final stroke, the working medium $\mathbf{Q}$ is thermalized with the reservoir $\mathbf{R}$, and the memory of the 1-bit meter used to measure the state of $\mathbf{C}$ is erased. The measurement outcome is discarded if the corresponding heat engine conditions \ref{['eq:heatEngCondSwitch1']}-\ref{['eq:heatEngCondSwitch3']} are not satisfied.
• Figure 2: Comparison of heat engine efficiencies in the coherent and incoherent modes of the quantum SWITCH for initially uncorrelated working medium and controller at $\beta\varepsilon = 0.1, 1, 10$.Top row: Efficiency gain $\Delta\eta_{\rm unc}^{\rm coh} = \tilde{\eta}_{\rm unc}^{\rm coh} - \eta_{\rm unc}^{\rm inc}$ as a function of the measurement strengths of $\mathbf{A}$ and $\mathbf{A}'$, where $\tilde{\eta}_{\rm unc}^{\rm coh}$ is optimized over the control state $\omega$, and $\eta_{\rm unc}^{\rm inc}$ is evaluated for the corresponding optimal $\omega$. Middle row: Efficiency $\eta_{\rm unc}^{(-)}$ associated with the post-selected outcome $\hbox{$| - \rangle$}_{\rm{c}}$, optimized over $\omega$. Bottom row: Efficiency $\eta_{\rm unc}^{(+)}$ for the post-selected outcome $\hbox{$| + \rangle$}_{\rm c}$, computed for the $\omega$ that maximizes $\eta_{\rm unc}^{(-)}$. In all panels, efficiencies are set to zero whenever the heat engine conditions on measurement strengths are not satisfied.
• Figure 3: Comparison of heat engine efficiencies in the coherent and incoherent modes of the quantum SWITCH for initially correlated separable states of the working medium and control system at $\beta\varepsilon = 0.1, 1, 10$.Top row: Efficiency gain $\Delta\eta_{\rm sep}^{\rm coh} = \tilde{\eta}_{\rm sep}^{\rm coh} - \eta_{\rm sep}^{\rm inc}$ as a function of the measurement strengths of $\mathbf{A}$ and $\mathbf{A}'$, where $\tilde{\eta}_{\rm sep}^{\rm coh}$ is optimized over the control state $\omega$, and $\eta_{\rm sep}^{\rm inc}$ is evaluated for the corresponding optimal $\omega$. Middle row: Efficiency $\eta_{\rm sep}^{(-)}$ corresponding to the post-selected outcome $\hbox{$| - \rangle$}_{\mathrm{c}}$, optimized over $\omega$. Bottom row: Efficiency $\eta_{\rm sep}^{(+)}$ corresponding to the post-selected outcome $\hbox{$| + \rangle$}_{\mathrm{c}}$, computed for the initial state that maximizes $\eta_{\rm sep}^{(-)}$. In all panels, efficiencies are set to zero whenever the heat engine conditions on the measurement strengths are not satisfied.
• Figure 4: Comparison of heat engine efficiencies in the coherent and incoherent modes of the quantum SWITCH for initially entangled working medium and controller at $\beta\varepsilon = 0.1, 1, 10$.Top row: Efficiency gain $\Delta\eta_{\rm qe}^{\rm coh} = \tilde{\eta}_{\rm qe}^{\rm coh} - \eta_{\rm qe}^{\rm inc}$ as a function of the measurement strengths of $\mathbf{A}$ and $\mathbf{A}'$, where $\tilde{\eta}_{\rm qe}^{\rm coh}$ is optimized over the control state $\omega$, and $\eta_{\rm qe}^{\rm inc}$ is evaluated for the corresponding optimal $\omega$. Middle row: Efficiency $\eta_{\rm qe}^{(-)}$ associated with the post-selected outcome $\hbox{$| - \rangle$}_{\rm{c}}$, optimized over $\omega$. Bottom row: Efficiency $\eta_{\rm qe}^{(+)}$ for the post-selected outcome $\hbox{$| + \rangle$}_{\rm c}$, computed for the initial state that maximizes $\eta_{\rm qe}^{(-)}$. In all panels, efficiencies are set to zero whenever the heat engine conditions on measurement strengths are not satisfied.
• Figure 5: Comparison of measurement outcome probabilities for different initial states. Measurement outcome probabilities $p^{(\pm)}$ of the control qubit $\mathbf{C}$ are shown as functions of the measurement strength $a$. The initial states satisfy $\theta = \frac{\pi}{2}$, $\phi = \frac{\pi}{4}$, $\phi' = 0$, and $(\beta\varepsilon)^{-1} = k_BT/\varepsilon=1.65\pm0.02$, and the measurement strengths satisfy $a' = 1 - a$. Experimental data are shown as symbols with error bars indicating statistical uncertainty, and the markers denote mean values. The red and blue elements correspond to the probabilities of the outcomes $\hbox{$| - \rangle$}_{\rm c}$ and $\hbox{$| + \rangle$}_{\rm c}$, respectively, shown for (a) the uncorrelated and (b) the separable or entangled initial states.