Reverse quantum speed limit: How slowly a quantum battery can discharge
Brij Mohan, Arun Kumar Pati
Abstract
We introduce the notion of a reverse quantum speed limit for arbitrary quantum evolution which answers a fundamental question: How slowly can a quantum system 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 the discharging process of quantum batteries, which answers the following question: How slowly can quantum batteries discharge? Our result provides a lower bound on the average discharging power of quantum batteries.