Interplay of Nonstabilizerness and Ergotropy in Quantum Batteries

TL;DR

This paper explores how nonstabilizerness influences work storage and charging power in quantum batteries, revealing symmetry-dependent correlations and scenarios where initial magic is unnecessary for optimal charging.

Contribution

It uncovers the relationship between nonstabilizerness and ergotropy in quantum batteries and shows that initial magic isn't always required for maximum charging power.

Findings

Ergotropy correlates with nonstabilizerness under U(1) symmetry-preserving interactions.

The correlation between nonstabilizerness and ergotropy is generally absent in non-symmetric interactions.

Maximum charging power can be achieved without initial nonstabilizerness, even with Clifford evolution.

Abstract

Nonstabilizerness plays an essential role in an efficient simulation of quantum systems on quantum computers. In this work, we investigate its role in the context of quantum batteries (QBs). To this end, we consider a system of N spin-1/2 particles, where the left half serves as the charger and the right half acts as the battery. By studying different classes of interactions between the charger and the battery, we quantify the amount of nonstabilizerness required to store work in the QB. Our results reveal that a one-to-one correspondence between the ergotropy stored in the battery and the total nonstabilizerness of the composite system emerges whenever the interaction Hamiltonian preserves a U(1) symmetry. In contrast, this correspondence is generally lost for more generic interactions that do not respect this symmetry. Finally, we examine the complementary scenario in which the battery is initialized in a nonstabilizer state and subsequently charged through Clifford evolution. In this case, we find that the maximum average charging power exhibits a non-monotonic dependence on the initial nonstabilizerness. Remarkably, the highest average power can be achieved even when the initial state carries no magic (nonstabilizerness), demonstrating that the initial magic is not a necessary resource for generating an optimal charging power in this protocol.