Complete quantum charging provides a sharp setting in which to ask how much multipartite entanglement is forced by speed itself. For a closed \(N\)-qubit battery evolving from \(\ket{\downarrow}^{\otimes N}\) to \(\ket{\uparrow}^{\otimes N}\) under a time-independent Hamiltonian, we exactly solve the pure-state depth-constrained speed problem. If the realized trajectory has entanglement depth at most \(k\), then the largest possible QSL-normalized rate \(η=τ_{\rm QSL}/T\) is \(η_{\max}(k)=\lceil N/k\rceil^{-1/2}\). Conversely, an observed rate \(η\) certifies trajectory entanglement depth at least \(\bigl\lceil N/\lfloor η^{-2}\rfloor\bigr\rceil\). The mechanism is block orthogonalization: under a fixed product partition, complete charging forces all blocks to orthogonalize simultaneously, and the quantum speed limit converts this counting constraint into the speed bound. Balanced cluster-flip evolutions saturate the bound, establishing an exact integer staircase frontier. Thus fast complete charging cannot be explained by many small independently charging blocks; in particular, crossing the threshold \(η>1/\sqrt2\) certifies, for \(N>1\), the generation of genuine \(N\)-partite entanglement.
Complete quantum charging provides a sharp setting in which to ask how much multipartite entanglement is forced by speed itself. For a closed (N)-qubit battery evolving from (\ket{\downarrow}^{\otimes N}) to (\ket{\uparrow}^{\otimes N}) under a time-independent Hamiltonian, we exactly solve the pure-state depth-constrained speed problem. If the realized trajectory has entanglement depth at most (k), then the largest possible QSL-normalized rate (η=τ_{\rm QSL}/T) is (η_{\max}(k)=\lceil N/k\rceil^{-1/2}). Conversely, an observed rate (η) certifies trajectory entanglement depth at least (\bigl\lceil N/\lfloor η^{-2}\rfloor\bigr\rceil). The mechanism is block orthogonalization: under a fixed product partition, complete charging forces all blocks to orthogonalize simultaneously, and the quantum speed limit converts this counting constraint into the speed bound. Balanced cluster-flip evolutions saturate the bound, establishing an exact integer staircase frontier. Thus fast complete charging cannot be explained by many small independently charging blocks; in particular, crossing the threshold (η>1/\sqrt2) certifies, for (N>1), the generation of genuine (N)-partite entanglement.
Collective quantum batteries (QBs) demonstrate remarkable acceleration in charging dynamics compared to their individual counterparts, underscoring the pivotal contribution of quantum correlations to advanced energy storage paradigms. A fundamental challenge lies in identifying QBs that exhibit genuine quantum advantages derived from multipartite entanglement. In this Letter, based on numerical and analytical evidence, we conjecture a universal bound on the charging rate for fully charging schemes, which is determined by the maximum entanglement depth arising during the charging dynamics. Here, the charging rate quantifies the intrinsic evolution speed of the charging process, appropriately normalized against the quantum speed limit (QSL). We analytically validate this conjecture in three distinct scenarios: (i) fully charging schemes saturating the QSL, (ii) fully parallel charging schemes, and (iii) the SU(2) fully charging schemes. Moreover, we establish a novel lower bound for entanglement depth detection, facilitating numerical verification of our proposed conjecture. By defining the genuine quantum charging advantage as the ratio between entanglement-enhanced charging rates and the maximum achievable non-entangling charging rate, we demonstrate that the charging rate constitutes a robust indicator of genuine quantum advantages.
We derive a quantum speed limit for ergotropy charging in the N-qubit Dicke battery. With the qubits initially in their ground state and the charger in a coherent state of mean photon number nˉ, the charging time to a target fraction ε of the maximum extractable work obeys, in the classical-field limit, ΓNτ∗(ε)≥arcsinε, where ΓN=2λnˉ/N is a single rate combining the light-matter coupling, the charger amplitude and the system size. The bound is geometric: although the ergotropy is defined by an optimisation over unitaries, it reduces to a fixed function of the angle swept by the collective spin on the Bloch sphere, and the drive bounds the rate at which that angle can grow, so the charging time is at least the required arc divided by the maximum angular velocity. The reduction rests on an exact statement about work extraction: only the coherent component of the drive delivers extractable work, while its vacuum fluctuations deposit energy that remains locked in the passive state. This makes the short-time coefficient independent of the charger occupation, and it is what separates a bound on extractable work from a bound on stored energy, which no instantaneous-power argument can supply. At finite charger occupation the inequality is tested rather than proved: numerical integration of the full Dicke Hamiltonian, with a dynamical charger and a mixed battery state, finds the bound respected at every admitted charging time for two to five qubits, and approached most closely in the limit of small target work. The familiar square-root estimate is the chord to this arc, recovered in the small-angle limit and weaker whenever a large fraction of the maximum work is required.
How fast an observable can evolve in time is answered by so-called observable speed limit. Here, we prove a stronger version of the observable speed limit and show that the previously obtained bound is a special case of the new bound. The stronger quantum speed limit for the state also follows from the stronger quantum speed limit for observables (SQSLO). We apply this to prove a stronger bound for the entanglement rate using the notion of capacity of entanglement (the quantum information theoretic counterpart of the heat capacity) and show that it outperforms previous bounds. Furthermore, we apply the SQSLO for the rate of modular Hamiltonian and in the context of interacting qubits in a quantum battery. These illustrative examples reveal that the speed limit for the modular energy and the time required to charge the battery can be exactly predicted using the new bound. This shows that for estimating the charging time of quantum battery SQSLO is actually tight, i.e., it saturates. Our findings can have important applications in quantum thermodynamics, the complexity of operator growth, predicting the time rate of quantum correlation growth, and quantum technology, in general.
The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this we derive exact quantum speed limits for the unitary dynamics of pure-state quantum systems that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity and yield a tighter quantum Cramér-Rao bound. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control, and quantum batteries.
We establish a general implementation-independent approach to assess the potential advantage of using highly entangled quantum states between the initial and final states of the charging protocol to enhance the maximum charging power of quantum batteries. It is shown that the impact of entanglement on power can be separated from both the global quantum speed limit associated with an optimal choice of driving Hamiltonian and the energy gap of the batteries. We then demonstrate that the quantum state advantage of battery charging, defined as the power obtainable for given quantum speed limit and battery energy gap, is not an entanglement monotone. A striking example we provide is that, counterintuitively, independent thermalization of the local batteries, completely destroying any entanglement, can lead to larger charging power than that of the initial maximally entangled state. Highly entangled states can thus also be potentially disadvantageous when compared to product states. We also demonstrate that taking the considerable effort of producing highly entangled states, such as W or k-locally entangled states, is not sufficient to obtain quantum-enhanced scaling behavior with the number of battery cells. Finally, we perform an explicit computation for a Sachdev–Ye–Kitaev battery charger to demonstrate that the quantum state advantage allows the instantaneous power to exceed its classical bound.
We investigate charging dynamics in many-body quantum batteries by examining the relationship between instantaneous charging power and the emergence of bipartite, tripartite, and multipartite quantum correlations across different battery--charger configurations. We find that the charging power reaches its maximum before the correlation measures peak, revealing a temporal separation between rapid energy transfer and the buildup of quantum correlations. We further study the role of interaction structure using local and many-body charging Hamiltonians for both unconstrained and constrained charging protocols, in which the total available charging resources are fixed to scale proportionally with the number of spins, thereby isolating the influence of interaction geometry and particle participation on the charging dynamics. In the unconstrained case, the enhanced charging energy observed for higher-order interactions originates primarily from the larger energy scale of the corresponding charging Hamiltonian. Under constrained conditions, however, increasing the interaction order alone provides no advantage over parallel charging when interaction and local spin-flip contributions are balanced, whereas interaction-dominated protocols significantly enhance charging performance, highlighting the importance of collective many-body dynamics. Fully collective interactions yield the largest enhancement in charging power together with stronger multipartite correlations, while partially collective interactions provide only limited improvements. Finally, extending the interaction range through next-nearest-neighbor couplings suppresses the charging power, demonstrating that, under constrained energetic resources, charging performance is governed primarily by interaction structure, particle participation, and collective many-body dynamics rather than by interaction order alone.