Reverse quantum speed limit and minimum Hilbert space norm

TL;DR

This paper explores how the reverse quantum speed limit, combined with a minimum time scale, imposes a lower bound on the change in quantum states, impacting interpretations of probability in quantum theory.

Contribution

It introduces a novel lower limit on the Hilbert space norm change derived from the reverse quantum speed limit and minimum time scale, with validation in specific models.

Findings

Lower bound on quantum state change norm established

Validation in two-state and ideal-measurement models

Implications for probability interpretation in quantum mechanics

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.