Quantum Speed Limit and optimal evolution time in a two-level system

TL;DR

This paper investigates the quantum speed limit in time-dependent two-level systems, specifically analyzing the Landau-Zener Hamiltonian, to understand the minimal evolution times in quantum control scenarios.

Contribution

It explores the relation between optimal control times and quantum speed limits in time-dependent two-level systems, an area less studied compared to time-independent cases.

Findings

Derived bounds for minimal evolution times in time-dependent systems.

Analyzed the Landau-Zener model in the context of quantum speed limits.

Provided insights into quantum control optimization.

Abstract

Quantum mechanics establishes a fundamental bound for the minimum evolution time between two states of a given system. Known as the quantum speed limit (QSL), it is a useful tool in the context of quantum control, where the speed of some control protocol is usually intended to be as large as possible. While QSL expressions for time-independent hamiltonians have been well studied, the time-dependent regime has remained somewhat unexplored, albeit being usually the relevant problem to be compared with when studying systems controlled by external fields. In this paper we explore the relation between optimal times found in quantum control and the QSL bound, in the (relevant) time-dependent regime, by discussing the ubiquitous two-level Landau-Zener type hamiltonian.