Charging a quantum battery through a collective non-adiabatic stroke stores energy in a shared bosonic mode, but part remains locked in correlations with the collective spin and is inaccessible to cyclic unitaries acting on the mode alone. A demon holding one bit can unlock this energy, quantified by the daemonic ergotropy. We investigate the value of one bit and its dependence on where the information is obtained. Two protocols are compared at matched stored energy and matched information, using balanced two-outcome measurements carrying exactly one bit. We find that one bit about the collective coordinate unlocks N ln(2) times as much work as one bit about a single ion. For three stored-energy settings and N = 4-24, the measured scaling exponent is 0.990 +/- 0.043, while double extrapolation gives a prefactor of 0.69298 +/- 0.00044, within 0.02% of ln(2). To leading order, the daemonic gain equals nu mu^2 times the between-outcome variance of Jx, verified numerically to 1.3%. A balanced single-ion measurement resolves 1/4 of this variance, whereas a balanced collective split resolves (ln(2)/4)N. The microscopic origin of the prefactor remains open; a Gaussian median-split estimate of 1/(2pi) is excluded by 9%. One bit recovers a constant fraction of the locked energy independent of N and yields roughly twice as much work per bit as a complete readout, indicating strong diminishing returns. We also show that unnormalized gain comparisons can reverse the conclusion and that the break-even ion number does not collapse onto the Dicke superradiant threshold when the mode frequency is varied.
Charging a quantum battery through a collective non-adiabatic stroke stores energy in a shared bosonic mode, but part remains locked in correlations with the collective spin and is inaccessible to cyclic unitaries acting on the mode alone. A demon holding one bit can unlock this energy, quantified by the daemonic ergotropy. We investigate the value of one bit and its dependence on where the information is obtained. Two protocols are compared at matched stored energy and matched information, using balanced two-outcome measurements carrying exactly one bit. We find that one bit about the collective coordinate unlocks N ln(2) times as much work as one bit about a single ion. For three stored-energy settings and N = 4-24, the measured scaling exponent is 0.990 +/- 0.043, while double extrapolation gives a prefactor of 0.69298 +/- 0.00044, within 0.02% of ln(2). To leading order, the daemonic gain equals nu mu^2 times the between-outcome variance of Jx, verified numerically to 1.3%. A balanced single-ion measurement resolves 1/4 of this variance, whereas a balanced collective split resolves (ln(2)/4)N. The microscopic origin of the prefactor remains open; a Gaussian median-split estimate of 1/(2pi) is excluded by 9%. One bit recovers a constant fraction of the locked energy independent of N and yields roughly twice as much work per bit as a complete readout, indicating strong diminishing returns. We also show that unnormalized gain comparisons can reverse the conclusion and that the break-even ion number does not collapse onto the Dicke superradiant threshold when the mode frequency is varied.
Charging a quantum battery through a pumped charger can lock a substantial part of its stored energy inside the bipartite correlations that grow between the constituent cells, and this \emph{correlation ergotropy}, being the energy that no local single-cell operation can reach and that only collective operations can recover, is the object of the present study. Following the charging trajectory of two coupled three-level cells, we find that the correlation ergotropy closely tracks the logarithmic negativity, which shows that the locked energy is carried by genuine bipartite entanglement rather than by coherent collective dynamics alone, and that an equal-strength coherent non-entangling drive produces no such locking at all. For a pure two-cell battery we establish an exact, basis-independent closed form in which the locked energy depends only on the sorted eigenvalues of the reduced cell and the cell energy levels, revealing that the locked fraction rises from zero at the separable corners of the Schmidt simplex to unity at the symmetric maximally entangled state and remains invariant under local unitaries. Decoherence and dephasing, which destroy the correlations, do \emph{not} release this energy but erase it, so extraction must be collective and must take place while the correlations persist, while cold damping leaves the effect intact and thermal occupation suppresses it. These results give a resource-theoretic reading of correlations in quantum batteries, sharpen the line between genuine entanglement and coherent collective dynamics, and point to experimentally accessible conditions for correlated-charge and collective-extraction protocols.
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.
Quantum batteries store energy in nonequilibrium quantum states. The ergotropy sets the work extractable by an arbitrary global unitary, but a device usually exchanges energy through a single local port. It remains unclear how much stored work such a port can deliver, and whether topological edge modes help. We study a dimerized spin chain of Su-Schrieffer-Heeger (SSH) type. Excited two-level ancillas charge it at one end by repeated collisions, and an initially empty two-level load discharges it at the same site. An exact free-fermion mapping yields a bound on the load work for all number-conserving quadratic extraction protocols. The load gains extractable work only if a single-particle mode of the battery holds more than half an excitation. Resonant charging fills the topological edge mode above this threshold. A single boundary pulse then delivers 98.6% of the maximal load work allowed by the bound for representative parameters. Under the same six-collision controls, the trivial-phase load remains passive. Within the protocol that selects the load pulse for maximum delivered work, cycle power peaks at a finite collision number while delivered work continues to increase over the scanned range. Over the tested range, the advantage survives hopping disorder, which preserves chiral symmetry. On-site disorder breaks this symmetry and leaves a finite fraction of loads passive. Topology thus supplies a localized access channel, while spectral matching and symmetry decide whether stored energy becomes usable local work.
We show that harnessing daemonic advantage is possible while charging a quantum battery by first time-evolving the battery collectively with an auxiliary charger, followed by an energy extraction via tracing out the charger. We define the difference between the minimum daemonic ergotropy and the maximum ergotropy of the battery as the daemonic gap at the time where the ergotropy of the battery is maximum. Considering a harmonic mode as the battery and a qubit as the auxiliary charger interacting via Jaynes-Cummings interaction, we show that the daemonic gap can be closed for specific initial passive states of the battery, including the ground state, truncated mixtures of low-lying states, and canonical thermal states. We further define the daemonic band as the difference between the maximum and the minimum daemonic ergotropy, and show that starting from the ground state of the single-mode battery, the daemonic band collapses. We also show that achieving a complete charging, along with accessing the full daemonic band, is possible for the single-mode battery using all of the other initial states by repeating the charging cycle and maximizing ergotropy in every round. We extend the battery-charger design to a multi-mode resonator battery and a qudit charger, and demonstrate, for a double-mode battery and a qutrit charger, that repeating the charging cycle is vital for simultaneously charging individual modes of the collective battery.
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(−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.
Ergotropic-gap relations provide thermodynamic witnesses of quantum correlations, but a direct dynamical connection between extractable work and entanglement remains largely unexplored in multipartite non-Gaussian bosonic systems. Here, we establish such a connection for a bosonic quantum battery driven by a coherent-state superposition. Despite the infinite-dimensional Hilbert space, the dynamics retains a simple structure that allows the relevant work and correlation measures to be obtained exactly. We show that the loss of extractable work associated with the passive part of the battery energy is directly determined by charger-battery entanglement. This relation also separates the charging power into contributions from energy transfer and from changes in the battery spectrum. At the same time, multipartite correlations are progressively redistributed from charger-involving correlations to correlations internal to the battery. For a symmetric resonant protocol, complete energy transfer coincides with charger-battery disentanglement and fully extractable stored energy, while multipartite correlations within the battery are maximal. Individual cells, however, remain mixed, revealing a distinction between global and local work extraction. We further show that, in the regime considered, locally extractable work is entirely supported by energetic coherence. Under single-photon loss, the analytical structure survives, but environmental correlations separate charger disentanglement from maximal work extraction.