Most energetic passive states

Harnessing Nth Root Gates for Energy Storage

We explore the use of fractional controlled-not gates in quantum thermodynamics. The Nth-root gate allows for a paced application of two-qubit operations. We apply it in quantum thermodynamic protocols for charging a quantum battery. Circuits for three (and two) qubits are analysed by considering the generated ergotropy and other measures of performance. We also perform an optimisation of initial system parameters, e.g.,the initial quantum coherence of one of the qubits strongly affects the efficiency of protocols and the system's performance as a battery. Finally, we briefly discuss the feasibility for an experimental realization.

Noncompletely Positive Quantum Maps Enable Efficient Local Energy Extraction in Batteries

Energy extraction from quantum batteries by means of completely positive trace-preserving (CPTP) maps leads to the concept of CPTP-local passive states, which identify bipartite states from which no energy can be squeezed out by applying any CPTP map to a particular subsystem. We prove, for arbitrary dimension, that if a state is CPTP-local passive with respect to a Hamiltonian, then an arbitrary number of copies of the same state-including an asymptotically large one-is also CPTP-local passive. We show further that energy can be extracted efficiently from CPTP-local passive states employing noncompletely positive trace-preserving (NCPTP) but still physically realizable maps on the same part of the shared battery on which operation of CPTP maps were useless. Moreover, we provide the maximum extractable energy using local-CPTP operations, and then, we present an explicit class of states and corresponding Hamiltonians, for which the maximum can be outperformed using physical local NCPTP maps. We provide a necessary and sufficient condition and a separate necessary condition for an arbitrary bipartite state to be unable to supply any energy using NCPTP operations on one party with respect to an arbitrary but fixed Hamiltonian. We build an analogy between the relative status of CPTP and NCPTP operations for energy extraction in quantum batteries, and the association of distillable entanglement with entanglement cost for asymptotic local manipulations of entanglement. The surpassing of the maximum energy extractable by NCPTP maps for CPTP-passive as well as for CPTP-nonpassive battery states can act as detectors of non-CPTPness of quantum maps.

Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Y. Luo et al., Phys. Rev. E 108, L052105 (2023)10.1103/PhysRevE.108.L052105], we derived a general bound on annealing performance by connecting annealing with stochastic thermodynamics tools, including a speed limit on state transformation from entropy production. We here describe the derivation of the general bound in detail. In addition, we analyze the case of simulated annealing with Glauber dynamics in depth. We show how to bound the two case-specific quantities appearing in the bound, namely the activity, a measure of the number of microstate jumps, and the change in relative entropy between the state and the instantaneous thermal state, which is due to temperature variation. We exemplify the arguments by numerical simulations on the Sherrington-Kirkpatrick (SK) model of spin glasses.

Study the charging process of moving quantum batteries inside cavity

In quantum mechanics, quantum batteries are devices that can store energy by utilizing the principles of quantum mechanics. While quantum batteries has been investigated largely theoretical, recent research indicates that it may be possible to implement such a device using existing technologies. The environment plays an important role in the charging of quantum batteries. If a strong coupling exists between the environment and the battery, then battery can be charged properly. It has also been demonstrated that quantum battery can be charged even in weak coupling regime just by choosing a suitable initial state for battery and charger. In this study, we investigate the charging process of open quantum batteries mediated by a common dissipative environment. We will consider a wireless-like charging scenario, where there is no external power and direct interaction between charger and battery. Moreover, we consider the case in which the battery and charger move inside the environment with a particular speed. Our results demonstrate that the movement of the quantum battery inside the environment has a negative effect on the performance of the quantum batteries during the charging process. It is also shown that the non-Markovian environment has a positive effect on improving battery performance.

Quantum ergotropy and quantum feedback control

We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy and charging bounds for unitary quantum operations. This implies that, in order to break the ergotropy bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy bound for unital quantum operations, applied to initial thermal equilibrium states, is tighter than the inequality representing the standard second law of thermodynamics without feedback control.

Quantum Energy Lines and the Optimal Output Ergotropy Problem

We study the transferring of useful energy (work) along a transmission line that allows for partial preservation of quantum coherence. As a figure of merit we adopt the maximum values that ergotropy, total ergotropy, and nonequilibrium free energy attain at the output of the line for an assigned input energy threshold. For phase-invariant bosonic Gaussian channel (BGC) models, we show that coherent inputs are optimal. For (one-mode) not phase-invariant BGCs we solve the optimization problem under the extra restriction of Gaussian input signals.

Stable charging of a Rydberg quantum battery in an open system

The charging of an open quantum battery is investigated where the charger and the quantum battery interact with a common environment. At zero temperature, the stored energy of the battery is optimal as the charger and the quantum battery share the same coupling strength (g_{C}=g_{B}). By contrast, in the presence of the quantum jump-based feedback control, the energy stored in the battery can be greatly enhanced for different couplings (g_{C}>g_{B}). Considering the feasibility of the experiment, a model of Rydberg quantum battery is proposed with cascade-type atoms interacting with a dissipative optical cavity. The effective coupling strength between the charger (quantum battery) and the cavity field is hence adjustable and one can make the battery close to perfect excitation. The adverse factors of charging quantum batteries such as time delay for feedback, finite temperature, and spontaneous emission of Rydberg atoms are also discussed, and the result shows that the quantum battery is still able to retain a satisfactory energy storage effect.

The tight Second Law inequality for coherent quantum systems and finite-size heat baths

In classical thermodynamics, the optimal work is given by the free energy difference, what according to the result of Skrzypczyk et al. can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and ideal energy storage that is able to extract work from coherences. Here we present the tight Second Law inequality, defined in terms of the ergotropy (rather than free energy), that incorporates both of those important microscopic effects - the locked energy in coherences and the locked energy due to the finite-size bath. The former is solely quantified by the so-called control-marginal state, whereas the latter is given by the free energy difference between the global passive state and the equilibrium state. Furthermore, we discuss the thermodynamic limit where the finite-size bath correction vanishes, and the locked energy in coherences takes the form of the entropy difference. We supplement our results by numerical simulations for the heat bath given by the collection of qubits and the Gaussian model of the work reservoir.

Entanglement, coherence, and charging process of quantum batteries

Quantum devices are systems that can explore quantum phenomena, such as entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as the main element in their high performance in powerful charging. In this paper, we explore quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two- and three-cell battery, our results suggest that entanglement is not the main resource in quantum batteries, where there is a nontrivial correlation-coherence tradeoff as a resource for the high efficiency of such quantum devices.

Structure of passive states and its implication in charging quantum batteries

In this article, in addition to the characterization of geometrical state spaces for the passive states, an operational approach has been introduced to distinguish them on their charging capabilities of a quantum battery. Unlike the thermal states, the structural instability of passive states assures the existence of a natural number n, for which n+1 copies of the state can charge a quantum battery while n copies cannot. This phenomenon can be presented in an n copy resource-theoretic approach, for which the free states are unable to charge the battery in n copies. Here we have exhibited the single copy scenario explicitly. We also show that general ordering of the passive states on the basis of their charging capabilities is not possible and even the macroscopic entities (viz. energy and entropy) are unable to order them precisely. Interestingly, for some of the passive states, the majorization criterion gives sufficient order to the charging and discharging capabilities. However, the charging capacity for the set of thermal states (for which charging is possible) is directly proportional to their temperature.

Stable and charge-switchable quantum batteries

A fully operational loss-free quantum battery requires an inherent control over the energy transfer process, with the ability of keeping the energy retained with no leakage. Moreover, it also requires a stable discharge mechanism, which entails that no energy revivals occur as the device starts its energy distribution. Here we provide a scalable solution for both requirements. To this aim, we propose a general design for a quantum battery based on an energy current (EC) observable quantifying the energy transfer rate to a consumption hub. More specifically, we introduce an instantaneous EC operator describing the energy transfer process driven by an arbitrary interaction Hamiltonian. The EC observable is shown to be the root for two main applications: (1) a trapping energy mechanism based on a common eigenstate between the EC operator and the interaction Hamiltonian, in which the battery can indefinitely retain its energy even if it is coupled to the consumption hub, and (2) an asymptotically stable discharge mechanism, which is achieved through an adiabatic evolution eventually yielding vanishing EC. These two independent but complementary applications are illustrated in quantum spin chains, where the trapping energy control is realized through Bell pairwise entanglement and the stability arises as a general consequence of the adiabatic spin dynamics.

Unifying paradigms of quantum refrigeration: Fundamental limits of cooling and associated work costs

In classical thermodynamics the work cost of control can typically be neglected. On the contrary, in quantum thermodynamics the cost of control constitutes a fundamental contribution to the total work cost. Here, focusing on quantum refrigeration, we investigate how the level of control determines the fundamental limits to cooling and how much work is expended in the corresponding process. We compare two extremal levels of control: first, coherent operations, where the entropy of the resource is left unchanged, and, second, incoherent operations, where only energy at maximum entropy (i.e., heat) is extracted from the resource. For minimal machines, we find that the lowest achievable temperature and associated work cost depend strongly on the type of control, in both single-cycle and asymptotic regimes. We also extend our analysis to general machines. Our work provides a unified picture of the different approaches to quantum refrigeration developed in the literature, including algorithmic cooling, autonomous quantum refrigerators, and the resource theory of quantum thermodynamics.

Unifying Paradigms of Quantum Refrigeration: A Universal and Attainable Bound on Cooling

Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm and complexity, and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers, with no general result that holds independent of assumptions. In this Letter we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.

Energetic instability of passive states in thermodynamics

Passivity is a fundamental concept in thermodynamics that demands a quantum system's energy cannot be lowered by any reversible, unitary process acting on the system. In the limit of many such systems, passivity leads in turn to the concept of complete passivity, thermal states and the emergence of a thermodynamic temperature. Here we only consider a single system and show that every passive state except the thermal state is unstable under a weaker form of reversibility. Indeed, we show that given a single copy of any athermal quantum state, an optimal amount of energy can be extracted from it when we utilise a machine that operates in a reversible cycle. This means that for individual systems, the only form of passivity that is stable under general reversible processes is complete passivity, and thus provides a physically motivated identification of thermal states when we are not operating in the thermodynamic limit.

Catalysis of heat-to-work conversion in quantum machines

We propose a hitherto-unexplored concept in quantum thermodynamics: catalysis of heat-to-work conversion by quantum nonlinear pumping of the piston mode which extracts work from the machine. This concept is analogous to chemical reaction catalysis: Small energy investment by the catalyst (pump) may yield a large increase in heat-to-work conversion. Since it is powered by thermal baths, the catalyzed machine adheres to the Carnot bound, but may strongly enhance its efficiency and power compared with its noncatalyzed counterparts. This enhancement stems from the increased ability of the squeezed piston to store work. Remarkably, the fraction of piston energy that is convertible into work may then approach unity. The present machine and its counterparts powered by squeezed baths share a common feature: Neither is a genuine heat engine. However, a squeezed pump that catalyzes heat-to-work conversion by small investment of work is much more advantageous than a squeezed bath that simply transduces part of the work invested in its squeezing into work performed by the machine.

Enhancing the Charging Power of Quantum Batteries

Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.