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arXiv:2609.24425

Quantum Work Extraction via Conditional Spatial Displacements

Necati Çelik

quant-phSubmitted Sep 21, 2026• Announced Sep 22, 2026• 0 citations
v1 · Sep 21, 2026v2 · Sep 28, 2026
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Abstract

We propose a protocol for extracting work from a coherent quantum battery state by exploiting measurement-assisted feedback mediated by a continuous-variable pointer. The scheme relies on the unitary operator $U = \exp(-i k t \, \hat{H} \otimes \hat{P}/\hbar)$, which generates entanglement between the battery's energy eigenstates and the position of an auxiliary pointer. A subsequent projective measurement of the pointer's position conditionally prepares the battery in a pure state from which work can be extracted via a feedback unitary. We analyze the protocol for a two-level quantum battery and a Gaussian pointer, computing the conditional states and the corresponding daemonic ergotropy. For the pure initial state considered, we find that the daemonic ergotropy equals the standard ergotropy for all interaction strengths, demonstrating that the measurement-assisted feedback recovers the full extractable work that would otherwise become inaccessible due to entanglement with the pointer when its degrees of freedom are traced out. The protocol thus provides a physically transparent realization of a quantum Maxwell demon, where the pointer acts as a quantum measurement ancilla whose position becomes correlated with the battery's energy. The scheme is amenable to experimental implementation in trapped-ion systems, and it contributes to the ongoing efforts to understand the role of quantum coherence and measurement in thermodynamics.

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We propose a protocol for extracting work from a coherent quantum battery state by exploiting measurement-assisted feedback mediated by a continuous-variable pointer. The scheme relies on the unitary operator U=exp⁡(−ikt H^⊗P^/ℏ)U = \exp(-i k t \, \hat{H} \otimes \hat{P}/\hbar)U=exp(−iktH^⊗P^/ℏ), which generates entanglement between the battery's energy eigenstates and the position of an auxiliary pointer. A subsequent projective measurement of the pointer's position conditionally prepares the battery in a pure state from which work can be extracted via a feedback unitary. We analyze the protocol for a two-level quantum battery and a Gaussian pointer, computing the conditional states and the corresponding daemonic ergotropy. For the pure initial state considered, we find that the daemonic ergotropy equals the standard ergotropy for all interaction strengths, demonstrating that the measurement-assisted feedback recovers the full extractable work that would otherwise become inaccessible due to entanglement with the pointer when its degrees of freedom are traced out. The protocol thus provides a physically transparent realization of a quantum Maxwell demon, where the pointer acts as a quantum measurement ancilla whose position becomes correlated with the battery's energy. The scheme is amenable to experimental implementation in trapped-ion systems, and it contributes to the ongoing efforts to understand the role of quantum coherence and measurement in thermodynamics.
Abstract The possibility of extracting more work from a physical system thanks to the information obtained from measurements has been a topic of fundamental interest in the context of thermodynamics since the formulation of the Maxwell’s demon thought experiment. We here consider this problem from the perspective of an open quantum battery interacting with an environment that can be continuously measured. By modeling it via a continuously monitored collisional model, we show how to implement the corresponding dynamics as a quantum circuit, including the final conditional feedback unitary evolution that allows to enhance the amount of work extracted. By exploiting the flexibility of IBM quantum computers and by properly modelling the corresponding quantum circuit, we experimentally simulate the work extraction protocol showing how the obtained experimental values of the daemonic extracted work are close to their theoretical upper bound quantified by the so-called daemonic ergotropy. We also demonstrate how by properly modelling the noise affecting the quantum circuit, one can improve the work extraction protocol by optimizing the corresponding extraction unitary feedback operation.
Abstract According to the Maxwell demon paradigm, additional work can be extracted from a classical or quantum system by exploiting information obtained through measurements on a correlated ancillary system. In the quantum setting, the maximum work extractable via unitary operations in such measurement-assisted protocols is referred to as daemonic ergotropy. In this work, we explore this concept in the context of continuous-variable quantum systems, focusing on Gaussian states and general-dyne (Gaussian) measurements. We derive a general expression for the daemonic ergotropy and examine two key scenarios: (i) bipartite Gaussian states where a general-dyne measurement is performed on one of the two parties, and (ii) open Gaussian quantum systems under continuous general-dyne monitoring of the environment. Remarkably, we show that for single-mode Gaussian states, the ergotropy depends solely on the state’s energy and purity. This enables us to express the daemonic ergotropy as a simple function of the unconditional energy and the purity of the conditional states, revealing that enhanced daemonic work extraction is directly linked to measurement-induced purification. We illustrate our findings through two paradigmatic examples: extracting daemonic work from a two-mode squeezed thermal state and from a continuously monitored optical parametric oscillator. In both case we identify the optimal general-dyne strategies that maximize the conditional purity and, in turn, the daemonic ergotropy.
The amount of extractable work from a physical system is fundamentally connected to the information available about its state, as illustrated by Maxwell's demon and the Gibbs paradox. In standard thermodynamic protocols involving system--bath interactions, the maximum work is given by the free-energy difference between the initial state and the corresponding Gibbs state at the bath temperature. This motivates a natural question: does information also limit work extraction in closed quantum systems that do not involve a heat bath and where work is obtained through unitary operations generated by a time-dependent Hamiltonian? While ergotropy quantifies the maximum work extractable via unitary operations, it assumes complete knowledge of the quantum state, typically requiring full state tomography. In realistic scenarios, however, only partial information is accessible. In this case, the relevant figure of merit is observational ergotropy, which depends explicitly on the measurement used to probe the system. We show that observational ergotropy decreases under classical post-processing of measurement outcomes, implying that fine-grained measurements allow greater work extraction than coarse-grained ones. Moreover, maximizing observational ergotropy over all possible measurements recovers standard ergotropy, which decomposes into incoherent (classical) and coherent (quantum) contributions. Our results demonstrate that coherence in the measurement projectors constitutes the key resource, enabling work extraction beyond the incoherent limit and establishing coherence as the origin of quantum advantage in observational ergotropy extraction.
The amount of work that can be extracted from a quantum system can be increased by exploiting the information obtained from a measurement performed on a correlated ancillary system. The concept of daemonic ergotropy has been introduced to properly describe and quantify this work extraction enhancement in the quantum regime. We here explore the application of this idea in the context of continuously monitored open quantum systems, where information is gained by measuring the environment interacting with the energy-storing quantum device. We first show that the corresponding daemonic ergotropy takes values between the ergotropy and the energy of the corresponding unconditional state. The upper bound is achieved by assuming an initial pure state and a perfectly efficient projective measurement on the environment, independently of the kind of measurement performed. On the other hand, if the measurement is inefficient or the initial state is mixed, the daemonic ergotropy is generally dependent on the measurement strategy. This scenario is investigated via a paradigmatic example of an open quantum battery: a two-level atom driven by a classical field and whose spontaneously emitted photons are continuously monitored via either homodyne, heterodyne, or photodetection.
We present a fully autonomous model of a mechanical Maxwell demon engine that converts heat absorbed by a qubit into population inversion in an attached quantum battery. A damped mechanical oscillator acts as a pointer that incorporates the essential demon function of information acquisition about the qubit state and subsequent feedback into the system dynamics, replacing external measurements and control operations. This is achieved by means of a Holstein-type Hamiltonian, which makes the pointer's equilibrium position depend on the qubit state and thereby induces a state-dependent resonance shift. The mechanism enables a selective energy transfer to an attached spin system that acts as the quantum battery. We derive both local and global Lindblad master equations for the coupled system and identify the parameter regimes in which the engine operates efficiently. The figure of merit is the resulting steady-state population inversion of the battery, quantified in terms of ergotropy. Based on these results, we discuss the necessary conditions for practical implementations of the demon engine on realistic experimental platforms.
Abstract The reduced state of a small system strongly coupled to a charger in thermal equilibrium may be athermal and used as a small battery once disconnected. By harnessing the battery-charger correlations, the battery’s extractable energy can increase above the ergotropy. We introduce a protocol that uses a quantum system as a memory that measures the charger and leaves the battery intact in its charged state. Using the information gained from the measurement, the daemonic ergotropy of the battery is extracted. Then the battery is reconnected to the charger, thermalizing and charging it. However, the memory should return to its initial standard state to close the thermodynamic cycle. Thus, on the one hand, the work cost of the cycle is the sum of the disconnecting and reconnecting battery-charger work plus the measurement and erasure work. On the other hand, the extracted energy is the daemonic ergotropy of the battery plus the ergotropy of the memory. The ratio of these quantities defines the efficiency of the cycle. The protocol is exemplified by a modified transverse spin 1/2 Ising chain, one spin functioning as the battery and the others as the charger. The memory is another auxiliary spin 1/2. We found pairs of measurement schemes from which we extract the same daemonic ergotropy from the battery, they dissipate the same amount of energy, and one leaves the memory in an active state, the other in a passive state. We study the memory’s ergotropy and the daemonic ergotropy of the battery. We find that with measurements, the efficiency can surpass that of the unmeasured protocol, given conditions on temperature, coupling, and choice of the measurement operators.