Quantum lower and upper speed limits using reference evolutions

Abstract We derive generalized quantum speed limit inequalities that represent limitations on the time evolution of states. They are extensions original inequality and applied to overlap between time-evolved state an arbitrary state. can discuss lower Bures angle, in addition upper as inequality, which allows us evaluate bounds processing for toward a target The written by using reference flexibly used obtain tight bound. demonstrate these properties twisted Landau–Zener model, Grover Hamiltonian, periodically-oscillating Hamiltonian.