Optimized daemonic ergotropy can make entanglement thermodynamically dispensable in measurement-assisted work extraction: for a fixed system marginal, quantum-classical states can reproduce the maximal work obtainable by optimizing the auxiliary measurement. We show that this equivalence is broken when the auxiliary measurement is randomized. For qudit-qubit quantum-classical states under Haar-random projective measurements, we derive upper bounds on the averaged daemonic gain and prove a gain-fluctuation trade-off, showing that any positive randomized gain necessarily entails measurement-induced fluctuations. In sharp contrast, a family of two-qubit entangled pure states attains the algebraic maximum of the gain allowed by a system marginal while remaining fluctuation-free for every measurement basis, yielding at least twice the gain achievable by any quantum-classical state with the same marginal. We further demonstrate that such conclusion holds when general two-qubit separable states are considered positioning randomized gain as a sufficient criterion for entanglement certification. Finally, we show that the entanglement advantage persists under partially randomized measurements sampled from a polar cap around the optimal basis. These results establish randomized daemonic ergotropy as a thermodynamic probe of entanglement and exhibit the connection between measurement-induced work fluctuations on the type of correlations: quantum entanglement vs classical.
Optimized daemonic ergotropy can make entanglement thermodynamically dispensable in measurement-assisted work extraction: for a fixed system marginal, quantum-classical states can reproduce the maximal work obtainable by optimizing the auxiliary measurement. We show that this equivalence is broken when the auxiliary measurement is randomized. For qudit-qubit quantum-classical states under Haar-random projective measurements, we derive upper bounds on the averaged daemonic gain and prove a gain-fluctuation trade-off, showing that any positive randomized gain necessarily entails measurement-induced fluctuations. In sharp contrast, a family of two-qubit entangled pure states attains the algebraic maximum of the gain allowed by a system marginal while remaining fluctuation-free for every measurement basis, yielding at least twice the gain achievable by any quantum-classical state with the same marginal. We further demonstrate that such conclusion holds when general two-qubit separable states are considered positioning randomized gain as a sufficient criterion for entanglement certification. Finally, we show that the entanglement advantage persists under partially randomized measurements sampled from a polar cap around the optimal basis. These results establish randomized daemonic ergotropy as a thermodynamic probe of entanglement and exhibit the connection between measurement-induced work fluctuations on the type of correlations: quantum entanglement vs classical.
Abstract We investigate how the presence of quantum correlations can influence work extraction in closed quantum systems, establishing a new link between the field of quantum non-equilibrium thermodynamics and the one of quantum information theory. We consider a bipartite quantum system and we show that it is possible to optimize the process of work extraction, thanks to the correlations between the two parts of the system, by using an appropriate feedback protocol based on the concept of ergotropy. We prove that the maximum gain in the extracted work is related to the existence of quantum correlations between the two parts, quantified by either quantum discord or, for pure states, entanglement. We then illustrate our general findings on a simple physical situation consisting of a qubit system.
Recently, the concept of daemonic ergotropy has been introduced to quantify the maximum energy that can be obtained from a quantum system through an ancilla-assisted work extraction protocol based on information gain via projective measurements [G. Francica et al., npj Quant. Inf. 3, 12 (2018)]. We prove that quantum correlations are not advantageous over classical correlations if projective measurements are considered. We go beyond the limitations of the original definition to include generalised measurements and provide an example in which this allows for a higher daemonic ergotropy. Moreover, we propose a see-saw algorithm to find a measurement that attains the maximum work extraction. Finally, we provide a multipartite generalisation of daemonic ergotropy that pinpoints the influence of multipartite quantum correlations, and study it for multipartite entangled and classical states.
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 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 address the problem of extracting work from a quantum system assisted by a quantum non-demolition (QND) energy measurement. When a perfect QND measurement can be performed and an auxiliary zero-temperature bath is available, the full energy of the quantum state can in principle be extracted even without any prior information on the input state. Owing to the presence of a zero-temperature bath, this is achieved at no energetic cost for the measurement process itself. On the contrary, here we consider what happens when the same protocol is implemented in non-ideal scenarios, specifically when the auxiliary bath has a finite temperature. In this case, not only is it impossible to extract the entire energy from the system, but the measurement strategy also acquires a non-zero energetic cost, accounting for both the interaction between system and measurement apparatus, and the corresponding Landauer erasure cost. We quantitatively assess the performance of these work-extraction protocols, both in absolute terms and through the so-called daemonic net gain, which explicitly includes the energetic cost of the measurement. We rigorously prove that, when access to a thermal bath is allowed in the extraction protocol, the daemonic net gain is always non-positive for any temperature of the auxiliary bath. Conversely, when only unitary operations are considered, the daemonic net gain can attain positive values. We further discuss these different figures of merit by analyzing a paradigmatic example for a single qubit system.
We investigate the decomposition of ergotropy into incoherent and coherent contributions for quantum systems subject to typical Markovian noise channels. The incoherent part originates from population inversion in the energy eigenbasis after dephasing, while the coherent part captures the role of quantum coherence in work extraction. For single-qubit systems, we derive explicit conditions for freezing and enhancement of coherent ergotropy and obtain an analytical upper bound, showing that it cannot exceed one half of the state's quantum coherence. We then study two classes of separable two-qubit states under local noise. For Bell-diagonal states, which are locally completely passive and possess no local coherence, we prove that the total extractable work equals the average of geometric quantum and classical correlations. In this case, coherent ergotropy cannot be enhanced, although freezing occurs under specific noise conditions. By contrast, for separable states with local coherence, coherent ergotropy can increase under all considered noise channels, including phase-flip and depolarizing noise. Extending the analysis to multipartite systems, we show that both the magnitude and range of noise-induced enhancement grow with the number of qubits, indicating collective reinforcement. Finally, we demonstrate through an explicit example that entanglement does not prevent this enhancement: coherent ergotropy may increase under noise even for entangled states. Our results reveal that noise can assist energy storage, challenging the conventional view of noise as purely detrimental and suggesting compatibility between noise-assisted enhancement and fast entanglement-based charging mechanisms in quantum batteries.