Work extraction in quantum finite systems is an important issue in quantum thermodynamics. The optimal work extracted is called ergotropy, and it is achieved by maximizing the average work extracted over all the unitary cycles. However, an agent that is non-neutral to risk is affected by fluctuations and should extract work by following the expected utility hypothesis. Thus, we investigate the optimal work extraction performed by a risk non-neutral agent by maximizing the average utility function over all the unitary cycles. We mainly focus on initial states that are incoherent with respect to the energy basis, achieving a probability distribution of work. In this case we show how the optimal work extraction will be performed with an incoherent unitary transformation, namely a permutation of the energy basis, which depends on the risk aversion of the agent. We give several examples, in particular also the work extraction from an ensemble of quantum batteries is examined. Furthermore, we also investigate how work extraction is affected by the presence of initial quantum coherence in the energy basis by considering a quasiprobability distribution of work.
Work extraction in quantum finite systems is an important issue in quantum thermodynamics. The optimal work extracted is called ergotropy, and it is achieved by maximizing the average work extracted over all the unitary cycles. However, an agent that is non-neutral to risk is affected by fluctuations and should extract work by following the expected utility hypothesis. Thus, we investigate the optimal work extraction performed by a risk non-neutral agent by maximizing the average utility function over all the unitary cycles. We mainly focus on initial states that are incoherent with respect to the energy basis, achieving a probability distribution of work. In this case we show how the optimal work extraction will be performed with an incoherent unitary transformation, namely a permutation of the energy basis, which depends on the risk aversion of the agent. We give several examples, in particular also the work extraction from an ensemble of quantum batteries is examined. Furthermore, we also investigate how work extraction is affected by the presence of initial quantum coherence in the energy basis by considering a quasiprobability distribution of work.
We consider a quasi-probability distribution of work for an isolated quantum system coupled to the energy-storage device given by the ideal weight. Specifically, we analyze a trade-off between changes in average energy and changes in weight's variance, where work is extracted from the coherent and incoherent ergotropy of the system. Primarily, we reveal that the extraction of positive coherent ergotropy can be accompanied by the reduction of work fluctuations (quantified by a variance loss) by utilizing the non-classical states of a work reservoir. On the other hand, we derive a fluctuation-decoherence relation for a quantum weight, defining a lower bound of its energy dispersion via a dumping function of the coherent contribution to the system's ergotropy. Specifically, it reveals that unlocking ergotropy from coherences results in high fluctuations, which diverge when the total coherent energy is unlocked. The proposed autonomous protocol of work extraction shows a significant difference between extracting coherent and incoherent ergotropy: The former can decrease the variance, but its absolute value diverges if more and more energy is extracted, whereas for the latter, the gain is always non-negative, but a total (incoherent) ergotropy can be extracted with finite work fluctuations. Furthermore, we present the framework in terms of the introduced quasi-probability distribution, which has a physical interpretation of its cumulants, is free from the invasive nature of measurements, and reduces to the two-point measurement scheme (TPM) for incoherent states. Finally, we analytically solve the work-variance trade-off for a qubit, explicitly revealing all the above quantum and classical regimes.
Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this nonequilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load.
Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite systems. In this framework, we consider a quantum battery made up of many interacting subsystems and study the maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting functional parallel ergotropy. Focusing on the bipartite case, we first observe that parallel ergotropy outperforms work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum available work and the second agent B, subsequently, extracts what is left on the other part. For the agents, this showcases the need of cooperating for an overall benefit. Second, from the informational point of view, we observe that the parallel capacity of a state can detect entanglement and compare it with the statistical entanglement witness that exploits fluctuations of stochastic work extraction. Additionally, we face the technical problem of computing parallel ergotropy. We derive analytical upper bounds for specific classes of states and Hamiltonians and provide recipes to obtain numerical upper bounds via semidefinite programming in the generic case. Finally, extending the concept of parallel ergotropy, we demonstrate that system's free-time evolution and application of local unitaries allow one to saturate the gap with the ergotropy of the whole system.
The study of quantum thermodynamics has led to the development of quantum batteries. These devices use quantum advantages to store and extract useful energy from physical systems. Ergotropy is the maximum work that can be extracted from a quantum system by cyclic unitary operations. When external thermal baths couple with the quantum battery, there is energy loss due to thermal effects on the system. In some cases, a part of the total energy available in the system cannot be stored as ergotropy. Therefore, it is important to consider the amount of residual energy that cannot be extracted as useful work from quantum batteries by unitary processes. To better understand the amount of energy lost during work extraction, it is necessary to examine the constraint of unitary processes. The system exergy represents the maximum amount of work that can be extracted from the system while bringing it into equilibrium with a thermal bath. It can be separated into two parts: ergotropy and residual energy. Thus, the present chapter describes the relationship between exergy and its potential benefits and effects on the performance of quantum batteries.
Quantum batteries are predicted to have the potential to outperform their classical counterparts and are therefore an important element in the development of quantum technologies. Of particular interest is the role of correlations in many-body quantum batteries and how these can affect the maximal work extraction, quantified by the ergotropy. In this paper we simulate the charging process and work extraction of many-body quantum batteries on noisy intermediate-scale quantum devices and devise the variational quantum ergotropy (VQErgo) algorithm, which finds the optimal unitary operation that maximizes work extraction from the battery. We test VQErgo by calculating the ergotropy of a many-body quantum battery undergoing transverse field Ising dynamics following a sudden quench. We investigate the battery for different system sizes and charging times and analyze the minimum number of ansatz circuit repetitions needed for the variational optimization using both ideal and noisy simulators. We also discuss how the growth of long-range correlations can hamper the accuracy of VQErgo in larger systems, requiring increased repetitions of the ansatz circuit to reduce error. Finally, we optimize part of the VQErgo algorithm and calculate the ergotropy on one of IBM's quantum devices. Published by the American Physical Society 2024
Fluctuations can challenge the possibility of improving work extraction from quantum correlations. This uncertainty in the work extraction process can be addressed by resorting to the expected utility hypothesis, which can provide an optimal method for work extraction. We study a bipartite quantum system and examine the role of quantum correlations in a daemonic work extraction performed by certain local operations and classical communication. Specifically, we demonstrate and explain how, depending on the so-called absolute risk aversion, a non-neutral risk agent, influenced by fluctuations, views quantum correlations differently from a neutral risk agent that is affected solely by the average work.