Quantum parameter estimation with the Landau-Zener transition

TL;DR

This paper explores the fundamental quantum limits of parameter estimation using Landau-Zener transitions, showing that quantum control and multiple passes can significantly enhance precision, with Fisher information scaling as high as T^4.

Contribution

It introduces quantum control techniques to Landau-Zener transitions, demonstrating enhanced parameter estimation precision and novel Fisher information scaling laws.

Findings

Quantum Fisher information scales as T^4 with control.

Proper quantum control improves estimation precision.

Multiple passes increase information about oscillation frequency.

Abstract

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time-independent if the transition probabilities alone are used. We add coherent control to the system, and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, "Landau-Zener-Stueckelberg interferometry", is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as $T^4$, where $T$ is the elapsed time.