Minimal time required to charge a quantum system

TL;DR

This paper introduces a geometric measure called quantum charging distance to determine the minimal time for charging quantum systems, providing bounds, advantages, and a new perspective on quantum battery charging speed.

Contribution

It defines the quantum charging distance, relates it to known bounds, and offers a measurable, eigenvalue-independent quantity to optimize quantum charging speed.

Findings

Quantum charging distance equals the Bures angle for pure states.

Provides bounds on the charging distance, aiding in quantum speed limit estimation.

Quantifies quantum charging advantage and improves understanding of quantum battery charging.

Abstract

We introduce a quantum charging distance as the minimal time that it takes to reach one state (charged state) from another state (depleted state) via a unitary evolution, assuming limits on the resources invested into the driving Hamiltonian. For pure states it is equal to the Bures angle, while for mixed states, its computation leads to an optimization problem. Thus, we also derive easily computable bounds on this quantity. The charging distance tightens the known bound on the mean charging power of a quantum battery, it quantifies the quantum charging advantage, and it leads to an always achievable quantum speed limit. In contrast with other similar quantities, the charging distance does not depend on the eigenvalues of the density matrix, it depends only on the corresponding eigenspaces. This research formalizes and interprets quantum charging in a geometric way, and provides a measurable quantity that one can optimize for to maximize the speed of charging of future quantum batteries.