Quantum batteries, devices that store energy in the excited states of quantum systems, attract attention due to collective effects that speed up charging. However, in realistic conditions, contact with a thermal reservoir leads to dissipation: ergotropy (extractable work) irreversibly leaks into the environment. Existing protection methods, such as frequent projective measurement in the spirit of the Zeno effect, require continuous observation and are difficult to implement. Weak measurements, in contrast, perturb the system gently and have already been used to protect entanglement from decoherence. This work transfers this tool to the thermodynamics of quantum batteries, adding the constraint of zero energy shift so that measurements do not recharge the battery.
The protocol consists of four steps. The battery, a qubit with energy gap ω, is prepared in an active state with excited-state population P₀ and coherence Q₀. Immediately after charging, a weak measurement with strength m is performed: it partially projects the system onto the ground state, reducing energy and ergotropy. The battery then evolves in contact with a thermal reservoir (temperature set by parameter f, damping rate γ) for time τ. A second weak measurement with strength w, inverse to the first, brings the system closer to the excited state. The key condition is zero net energy shift $ε_{mw}$(τ)=0 and zero ergotropy shift $W_{mw}$(τ)=0. For given m, P₀, f, and γ, the strength w is chosen analytically from equation (24). Working points are additionally verified numerically for a two-qubit system with a common reservoir.
For a single qubit with P₀=0.9, m=0.4, w≈0.2, τ=τ_γ (characteristic decay time), and f=0.3, the protocol yields an ergotropy gain $R_{mw}$(τ_γ)≈0.76ω×10⁻¹, which is 8.57% of the initial charge. The incoherent part contributes the most (≈0.71ω×10⁻¹), while the coherent part contributes a smaller but positive amount (≈0.5ω×10⁻²) for initial coherence |Q₀|²≈7.67×10⁻². The postselection success probability is Π≈0.57. At lower temperature (f=0.15), working points shift to larger m (≈0.95–1) and P₀ (≈0.8–1), and gain and probability are inversely related: stronger measurements give larger gain but succeed less often. For a two-qubit battery with a common reservoir and an X-state, the protocol also works: with q=0.1 (no initial entanglement), the gain R(τ_γ)≈0.49ω×10⁻¹ (6.12% of charge) with probability 0.37; with q=0.9 (with entanglement), the gain R(τ_γ)≈6.1ω×10⁻¹ (75.81% of charge) with probability 0.09. Coherent ergotropy can temporarily increase during dissipation if the population passes through 1/2, reminiscent of an ergotropic analogue of the Mpemba effect.
This work shows that weak measurements can be embedded in the thermodynamic cycle of a quantum battery without net energy input, provided constraints on energy and ergotropy shifts are imposed. This distinguishes the approach from neighboring works on state protection, where measurements were used to suppress decoherence without considering thermodynamic balance. Here, the zero energy shift guarantees that the ergotropy gain is not hidden recharging but arises from the different discharge rates of states with different populations. Furthermore, it is demonstrated for the first time that the coherent part of ergotropy can contribute positively to the gain under certain parameters, although its scale is an order of magnitude smaller than the incoherent part.
The protocol can be extended to strongly coupled qubits, where the local master equation is inapplicable and a global description is required. It is interesting to explore the role of quantum correlations, such as entanglement and quantum discord, when scaling to N cells. It is also important to account for the energy cost of the measurements themselves, in the spirit of Landauer's principle, to assess the full thermodynamic benefit. Adaptive protocols that adjust measurement strength to changing environmental conditions could expand the range of working parameters.
The method is applicable in quantum energy storage technologies, from superconducting qubits to NMR systems. It also provides a tool for managing dissipation in other open quantum systems where coherence protection is important.
Test the protocol experimentally on NMR or superconducting circuit platforms, where weak measurements are already implemented. Optimize parameters for specific noise models and temperatures.
A key problem in quantum thermodynamics is stabilizing ergotropy in open systems. This work directly links protection from dissipation to the energy balance of measurements, bridging the gap between state-protection protocols and thermodynamic constraints. An open question remains about the minimal energy cost of information obtained from weak measurements and its impact on the overall battery efficiency.
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What the work does
The authors propose a protocol of two weak measurements to protect a quantum battery from dissipation: the first measurement weakens the coupling to the reservoir, and the second restores the state after partial discharge. By tuning the measurement strengths so that the total energy and ergotropy shifts are zero, they demonstrate preservation of up to 8.57% of the charge for one- and two-qubit systems on NMR and superconducting circuit platforms.
Where its strength is
The key strength of the work is the introduction of the zero energy shift constraint, which ensures that the measurements do not recharge the battery but only protect it from losses. This makes the protocol thermodynamically honest and potentially implementable on current quantum devices.
Where it could go next
Worth trying
Why this may matter
The developed protocol offers a practical way to extend the energy storage time in quantum batteries without external recharging, which is important for future quantum technologies where energy efficiency is critical.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.59, against a usual 0.64. It looks like few have drilled nearby.
The Mpemba effect, the observation that hot water sometimes freezes faster than cold water, has an ergotropic analogue: a battery with lower initial population can discharge more slowly than a fully charged one. This work exploits that property for gain: a weak measurement places the battery in a state with lower population, which loses energy more slowly.
The idea of a quantum battery charged and protected by measurements echoes the concept of a 'quantum fuse' from science fiction, where an observer influences the state of a system. In the series 'Orphan Black', quantum effects are used to control biological processes, although there is no direct analogy to the weak-measurement protocol.