Parallel ergotropy: Maximum work extraction via parallel local unitary operations

TL;DR

This paper introduces parallel ergotropy, a measure of maximum work extractable via local unitaries in multipartite quantum systems, showing it outperforms egoistic strategies, detects entanglement, and can be computed with bounds and numerical methods.

Contribution

It defines and analyzes parallel ergotropy, demonstrating its advantages over local strategies, its informational significance for entanglement detection, and providing methods for its calculation.

Findings

Parallel ergotropy outperforms egoistic work extraction strategies.

Parallel ergotropy can detect entanglement in quantum states.

Analytical and numerical bounds for parallel ergotropy are derived.

Abstract

Maximum quantum work extraction is generally defined in terms of the ergotropy functional, no matter how experimentally complicated is the implementation of the optimal unitary allowing for it, especially in the case of multipartite systems. In this framework, we consider a quantum battery made up of many interacting sub-systems and study the maximum extractable work via concurrent local unitary operations on each subsystem. We call the resulting functional parallel ergotropy. Focusing on the bipartite case, we first observe that parallel ergotropy outperforms work extraction via egoistic strategies, in which the first agent A extracts locally on its part the maximum available work and the second agent B, subsequently, extracts what is left on the other part. For the agents, this showcases the need of cooperating for an overall benefit. Secondly, from the informational point of view, we observe that the parallel capacity of a state can detect entanglement and compare it with the statistical entanglement witness that exploits fluctuations of stochastic work extraction. Additionally, we face the technical problem of computing parallel ergotropy. We derive analytical upper bounds for specific classes of states and Hamiltonians and provide receipts to obtain numerical upper bounds via semi-definite programming in the generic case. Finally, extending the concept of parallel ergotropy, we demonstrate that system's free-time evolution and application of local unitaries allow one to saturate the gap with the ergotropy of the whole system.