Universally charging protocols for quantum batteries: A no-go theorem

The effectiveness of a quantum battery relies on a robust charging process, yet these are often sensitive to the 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 auxiliary quantum systems. To that end, we prove a no-go theorem that 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 Hamiltonians. 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.