Reverse quantum speed limit: How slowly a quantum battery can discharge

Abstract

We introduce the notion of reverse quantum speed limit for arbitrary quantum evolution which answers a fundamental question: ``how slow a quantum system can evolve in time?" Using the geometrical approach to quantum mechanics, the reverse speed limit follows from the fact that the gauge invariant length of the reference section is always greater than the Fubini-Study distance on the projective Hilbert space of the quantum system. We illustrate the reverse speed limit for two-level quantum systems with an external driving Hamiltonian and show that our results hold well. We find several examples where our bound is tight. We also find one practical application of the reverse speed limit in discharging process of quantum batteries which answers the question: ``how slow quantum batteries can discharge?" Our result provides a lower bound on the average discharging power of quantum batteries.