Abstract Quantum error correction (QEC) protects logical information, whereas a quantum battery is judged by the work it can deliver. We ask when a recovery operation applied during storage may be credited with protecting a battery's ergotropy. The second law bounds the average work of each recovery call from below by the change of nonequilibrium free energy it causes at bath temperature T; as a storage convention we debit the nonnegative part of this change and take the net ergotropy gain left per call as the budget for all further overhead. We apply this ledger to batteries of two to four two-level cells under collective and independent Lindblad noise, testing a coherence-restoring heuristic, the four-qubit [[4,1,2]] amplitude-damping code with two recovery completions, standard channel families, and reset channels. Every state in the code space of the [[4,1,2]] code has zero mean energy and at most half the maximal ergotropy, so a decoder that restores the code space cannot protect a fully charged battery; a completion that leaves the rest of the Hilbert space untouched avoids this bound but still loses ergotropy on a fully charged battery during storage. Unital recoveries cannot raise the ergotropy by more than the energy they supply. For four cells and inputs diagonal in the energy basis, an optimal energy-nonincreasing covariant recovery is attained by a reset channel, whose value we give in closed form and whose gain comes from removing entropy. At 10 mK and 10 GHz the tested recoveries leave at most 3.3×10⁻² energy quanta per call beyond the debit, less than one photon at the cell frequency, so any implementation that dissipates a single quantum per call beyond the debit loses ergotropy.
Abstract Quantum error correction (QEC) protects logical information, whereas a quantum battery is judged by the work it can deliver. We ask when a recovery operation applied during storage may be credited with protecting a battery's ergotropy. The second law bounds the average work of each recovery call from below by the change of nonequilibrium free energy it causes at bath temperature T; as a storage convention we debit the nonnegative part of this change and take the net ergotropy gain left per call as the budget for all further overhead. We apply this ledger to batteries of two to four two-level cells under collective and independent Lindblad noise, testing a coherence-restoring heuristic, the four-qubit [[4,1,2]] amplitude-damping code with two recovery completions, standard channel families, and reset channels. Every state in the code space of the [[4,1,2]] code has zero mean energy and at most half the maximal ergotropy, so a decoder that restores the code space cannot protect a fully charged battery; a completion that leaves the rest of the Hilbert space untouched avoids this bound but still loses ergotropy on a fully charged battery during storage. Unital recoveries cannot raise the ergotropy by more than the energy they supply. For four cells and inputs diagonal in the energy basis, an optimal energy-nonincreasing covariant recovery is attained by a reset channel, whose value we give in closed form and whose gain comes from removing entropy. At 10 mK and 10 GHz the tested recoveries leave at most 3.3×10⁻² energy quanta per call beyond the debit, less than one photon at the cell frequency, so any implementation that dissipates a single quantum per call beyond the debit loses ergotropy.
We ask whether the [[5,1,3]] holographic quantum error-correcting code — previously shown to protect logical correlations under independent physical noise — also protects a quantum battery's extractable work (ergotropy), and whether entangling multiple logical-qubit batteries during charging gives a genuine collective advantage. Part I finds a two-regime result for a single logical qubit: holographic encoding protects ergotropy strongly for noise p<0.36 (z-scores up to +5.8) but the advantage inverts catastrophically above that threshold (z-scores down to −5.0); active syndrome-based recovery removes the threshold entirely. Part II extends the question to N=2–8 entangled logical qubits. Three real methodological errors were caught and corrected en route before a trustworthy answer emerged: optimized entangling coupling gives a real, reproducible ≈2× collective advantage that shrinks monotonically with N, the opposite of the growing scaling predicted in the broader literature — corroborated by an independent ansatz and a symmetry-breaking control. Finally, collective charging's speed advantage is shown not to transfer to noise robustness. Simulation-stage results (exact state-vector and density-matrix simulation); hardware validation proposed as future work.
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.
Ergotropy--a key figure of merit for quantum battery (QB) performance--plays a crucial role. However, the dynamics and physical mechanisms governing ergotropy evolution remain open challenges. Here, we investigate the ergotropy of a general QB model and find that the charging process is accompanied by the variation and inversion of the energy level populations. In the absence of population inversion, the ergotropy is fully consistent with coherent ergotropy; in local and global population inversion, it is determined by both coherent and incoherent ergotropy. Via random sampling of quantum states and Hamiltonians, we show that coherence and the participation ratio enhance coherent ergotropy, whereas incoherent ergotropy--whether enhanced, unchanged, or suppressed--depends on diagonal entropy, the participation ratio, and energy level population ordering. We demonstrate that the ergotropy lower bound is incoherent ergotropy, the upper bound is the QB stored energy, and enhanced QB purity suppresses locked energy and boosts charging efficiency. Furthermore, we use the Tavis-Cummings (TC) and Jaynes-Cummings (JC) batteries as paradigms to validate our findings. Our work elucidates ergotropy underlying mechanisms in general QBs and establishes a rigorous framework for optimizing ergotropy and charging efficiency, paving the way for high-performance quantum energy-storage devices.
Quantum batteries are emerging as highly efficient energy-storage devices that can exceed classical performance limits. Although there have been significant advancements in controlling these systems, challenges remain in stabilizing stored energy and minimizing losses due to inevitable environmental interaction. In this paper, we propose a protocol that employs selective weak measurements to protect quantum states from such influence and mitigate battery discharging and that is feasible in state-of-the-art technologies. We establish thermodynamic constraints that allow this method to be implemented without disrupting the overall energy and ergotropy balance of the system, i.e., with no extra net recharging. Our findings demonstrate that appropriately chosen measurement intensity can reduce unwanted discharging effects, thereby preserving ergotropy and improving the stability of quantum batteries. We illustrate the protocol with single- and two-qubit systems and establish the generalization for N -cell batteries. Additionally, we explore how weak measurements influence the coherent and incoherent components of ergotropy, providing new insights into the practical application of quantum coherence in energy-storage technologies.
Quantum batteries utilize nonclassical resources to achieve charging speed and energy storage performances that surpass classical thermodynamic limits. However, the practical realization of quantum batteries is often constrained by the inevitable environment-induced dissipation of both stored ergotropy and coherence. To actively counteract these losses, we propose a dual-channel coherence framework that exploits dark-state protection to stabilize ergotropy. We conduct, for the first time, an investigation of the synergistic interplay between internal charger coherence and reservoir squeezing, the latter acting as a source of external coherence. In the resource-efficient regime where charger and battery sizes are comparable, our study shows that internal charger coherence and reservoir squeezing jointly enhance the transient charging power. Crucially, initial charger coherence is the fundamental resource for maximizing and stabilizing steady-state ergotropy through dark-state protection. Our analysis reveals that these advantages are driven by the buildup of local battery coherence, which emerges from the integration of both internal and external coherence sources. These results offer a robust pathway for high-power, stabilized energy storage in quantum architectures.
We study the ergotropy and the thermodynamic potentials of a qubit battery charged by repeated interactions with clusters of thermal ancillas, qubits or oscillators, through a composite system-bath coupling that generates steady-state coherence in the energy basis. A single parameter encoding the bath quantum statistics yields the coherence and ergotropy in closed form for any cluster size. For large clusters, the ergotropy becomes independent of the bath statistics and, at optimal couplings, reaches a universal fraction of the equilibrium internal energy of the qubit at the bath temperature. Since the charged state has no population inversion, all extractable work comes from coherence. The ergotropy is flat at low temperatures. We trace this plateau to the third law, and show that the ergotropy is proportional to the equilibrium enthalpy of the qubit, whose slope vanishes with the heat capacity. For a battery composed of multiple qubits, the coherence grows exponentially with the number of qubits while the ergotropy grows linearly, both remaining a nearly constant fraction of their respective maxima. The charged state is a non-equilibrium steady state with finite entropy at zero temperature, sustained by the work of switching the collisional interaction on and off. The cost is nonzero whenever the parallel coupling is nonzero, and, unlike the ergotropy, it depends on the bath statistics.