Scattering as a quantum metrology problem: a quantum walk approach

TL;DR

This paper models quantum particle scattering by a barrier as a quantum walk, using quantum Fisher information to optimize barrier height estimation, and identifies nearly optimal measurement strategies.

Contribution

It formalizes scattering as a quantum walk problem and applies quantum Fisher information to optimize parameter estimation in this context.

Findings

Quantum Fisher information depends on wave packet parameters but less so on signal-to-noise ratio.

Dichotomic position measurement is nearly optimal for detection.

Reflection and transmission probabilities are derived for the scattering process.

Abstract

We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher information as a mean to quantify the maximal possible accuracy in the estimation of the height of the barrier. We introduce suitable initial states of the walker and derive the reflection and transmission probabilities of the scattered state. We show that while the quantum Fisher information is affected by the width and central momentum of the initial wave packet, this dependency is weaker for the quantum signal-to-noise ratio. We also show that a dichotomic position measurement provides a nearly optimal detection scheme.