Quantum lower and upper speed limits

Abstract

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

12 pages

References in corpus (7)

• The Magnus expansion and some of its applications
• Quantum Computation as Geometry
• Quantum speed limits in open system dynamics
• Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential
• Reverse Quantum Speed Limit: How Slow Quantum Battery can Discharge?
• General bound on the performance of counter-diabatic driving acting on dissipative spin systems
• Bounds on quantum adiabaticity in driven many-body systems from generalized orthogonality catastrophe and quantum speed limit

Cited by in corpus (7)

• Speed limits of the trace distance for open quantum system
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Entanglement-assisted quantum speedup: Beating local quantum speed limits
• Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes
• Quantum dynamical speedup for correlated initial states
• A Unifying Quantum Speed Limit For Time-Independent Hamiltonian Evolution
• Implementation of multiparticle quantum speed limits on observables