Fixed Point Engineering of Quantum Batteries

Abstract

We develop, in the context of open quantum systems, a general formalism to build completely positive and unital (CPU) maps that have a desired fixed point. In contrast to quantum channels, these maps act on observables, not on states. As the CPU maps will have a known observable as their fixed point, we know by construction that in the asymptotic limit the map will yield a constant observable. Therefore, if we implement this in a differential equation, we have a linear growth of a quantity with respect to time. Applying these ideas to the charging of quantum batteries, we obtain an upper bound on the charging power of batteries by allowing interchanges of multiple states every time the CPU map is applied.

8 pages