Tight lower bounds on the time it takes to generate a geometric phase

Niklas Hörnedal, Ole Sönnerborn

Published 2023-05-20Version 1

Although the non-adiabatic Aharonov-Anandan geometric phase acquired by a cyclically evolving quantum system does not depend on the evolution time, it does set a lower bound on the evolution time. In this paper, we derive three tight bounds on the time required to generate any prescribed Aharonov-Anandan geometric phase. The derivations are based on recent results on the geometric character of the classic Mandelstam-Tamm and Margolus-Levitin quantum speed limits.