Frozen and growing quantum work under noise: Coherence and correlations as key resources
Phys. Rev. A 113, 032220 – Published 26 March, 2026
DOI: https://doi.org/10.1103/43vv-521p
Abstract
We explore the decomposition of ergotropy into incoherent and coherent parts for quantum systems exposed to typical Markovian noise channels. The incoherent contribution arises from population inversion in the energy eigenbasis after dephasing, while the coherent contribution reflects the impact of quantum coherence on work extraction. For single-qubit systems, we derive explicit conditions for freezing and even enhancement of the coherent work and establish an analytical upper bound, showing that the coherent contribution cannot exceed one-half of the state’s quantum coherence. We then analyze two distinct classes of separable two-qubit states, where both qubits are affected by noise. For Bell-diagonal states—locally completely passive and therefore lacking local coherence—we prove a theorem establishing that the total extractable work under noise equals the average of the geometric quantum and classical correlations. In this case, no enhancement of coherent ergotropy occurs, although specific freezing behavior is identified under certain noise conditions. In contrast, for separable states endowed with local coherence, coherent ergotropy can increase under all investigated noises, even phase flip and depolarizing channels that are typically expected to destroy coherence. Extending to multipartite systems, we find that both the magnitude and the range of noise-induced enhancement scale with the number of qubits, revealing a collective reinforcement of the coherent ergotropy. Finally, we show by means of an explicit example that entanglement does not preclude this enhancement, and that coherent ergotropy can increase under noise even for entangled states. These findings provide novel insights into how noise can be leveraged in quantum systems for energy storage, contrary to the conventional perspective, suggesting that noise-assisted enhancement of stored energy can coexist with fast-charging mechanisms typically enabled by entangling operations in quantum batteries.
