Energy storage and coherence in closed and open quantum batteries

TL;DR

This paper investigates how quantum coherence influences energy storage in quantum batteries, establishing bounds on energy exchange based on coherence measures, with applications to specific quantum models.

Contribution

It introduces bounds on energy storage in quantum batteries using coherence measures, applicable to both closed and open systems, and demonstrates these bounds on various models.

Findings

Energy storage is bounded by Hilbert-Schmidt coherence.

Bounds are also derived from Hamiltonian coherence via commutators.

Applications to quantum systems like the XY model and Spin-Boson model confirm the bounds.

Abstract

We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case.