Local passivity and entanglement in shared quantum batteries

TL;DR

This paper explores the relationship between local passivity, entanglement, and work extraction in shared quantum batteries, revealing how entanglement influences the amount of energy that can be globally or locally extracted.

Contribution

It establishes conditions for local passivity in shared quantum batteries and links entanglement to the maximum extractable work under local and global operations.

Findings

Locally passive states relate to their entanglement content.

Work extraction deficit equals the optimal global work for pure states.

Maximum globally extractable work corresponds to the maximum locally extractable work for fixed entanglement.

Abstract

We identify the conditions for local passivity for shared quantum batteries with local Hamiltonians. For locally passive states of two-qubit batteries, we find the relation of their entanglement content with the amount of energy that can be globally extracted from them. Moreover, we obtain that the deficit in work extraction from pure battery states due to the restriction to local unitaries is equal to the amount of optimal global work extractable from the corresponding pure locally passive battery state, for the same entanglement supply. Furthermore, the pure battery state for which globally extractable work attains a maximum, among the set of all pure states with a fixed value of entanglement, also provides the maximum locally extractable work.