Universally-Charging Protocols for Quantum Batteries: A No-Go Theorem

TL;DR

This paper proves that universally-charging protocols are impossible for closed quantum batteries with finite dimensions and cannot be physically generated for infinite dimensions, but are feasible in open quantum systems.

Contribution

It establishes a no-go theorem for universal charging in closed quantum batteries and explores conditions for universal protocols in open quantum systems.

Findings

UC protocols are impossible for finite-dimensional closed quantum batteries.

Physically reasonable Hamiltonians cannot generate UC operators in infinite-dimensional cases.

Non-unitary UC protocols are possible in open quantum batteries.

Abstract

The effectiveness of a quantum battery relies on a robust charging process, yet these are often sensitive to initial state of the battery. We introduce the concept of a universally-charging (UC) protocol, defined as one that either increases or maintains the average battery energy for all initial states, without ever decreasing it. We show that UC protocols are impossible for closed quantum batteries, thus necessitating interactions with auxilliary quantum systems. To that end, we prove a no-go theorem which prohibits UC protocols for closed quantum batteries with finite-dimensional Hilbert spaces. Leveraging a no-go theorem for topological quantum walks, we argue that even for infinite-dimensional Hilbert spaces, while unitary UC operators exist, they cannot be generated by physically reasonable Hamiltonian protocols. However, regardless of the dimension, non-unitary UC protocols can be achieved in open quantum batteries. To illustrate this, we present a general model with a control qubit, whose state interpolates between universal-charging and universal-discharging protocols.