Frozen and Growing Quantum Work under Noise: Coherence and Correlations as Key Resources

TL;DR

This paper explores how quantum coherence and correlations influence work extraction in noisy quantum systems, revealing that noise can sometimes enhance energy storage and that entanglement does not hinder this process.

Contribution

It provides analytical conditions for freezing and enhancing coherent ergotropy under noise, and shows noise-induced work enhancement occurs even in entangled states.

Findings

Coherent ergotropy is bounded by quantum coherence.

Noise can increase work extraction in separable states with local coherence.

Entanglement does not prevent noise-assisted energy enhancement.

Abstract

We investigate the decomposition of ergotropy into incoherent and coherent contributions for quantum systems subject to typical Markovian noise channels. The incoherent part originates from population inversion in the energy eigenbasis after dephasing, while the coherent part captures the role of quantum coherence in work extraction. For single-qubit systems, we derive explicit conditions for freezing and enhancement of coherent ergotropy and obtain an analytical upper bound, showing that it cannot exceed one half of the state's quantum coherence. We then study two classes of separable two-qubit states under local noise. For Bell-diagonal states, which are locally completely passive and possess no local coherence, we prove that the total extractable work equals the average of geometric quantum and classical correlations. In this case, coherent ergotropy cannot be enhanced, although freezing occurs under specific noise conditions. By contrast, for separable states with local coherence, coherent ergotropy can increase under all considered noise channels, including phase-flip and depolarizing noise. Extending the analysis to multipartite systems, we show that both the magnitude and range of noise-induced enhancement grow with the number of qubits, indicating collective reinforcement. Finally, we demonstrate through an explicit example that entanglement does not prevent this enhancement: coherent ergotropy may increase under noise even for entangled states. Our results reveal that noise can assist energy storage, challenging the conventional view of noise as purely detrimental and suggesting compatibility between noise-assisted enhancement and fast entanglement-based charging mechanisms in quantum batteries.