Reverse quantum speed limit and minimum Hilbert space norm

Abstract: The reverse quantum speed limit (RQSL) gives an upper limit to the time for evolution between initial and final quantum states. We show that, in conjunction with the existence of a minimum time scale, the RQSL implies a lower limit to the norm of the change in a quantum state, and confirm that this limit is satisfied in two-state and ideal-measurement models. Such a lower limit is of relevance for interpretational issues in probability and for understanding the meaning of probability in Everett quantum theory.