Scattering as a quantum metrology problem: a quantum walk approach

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.

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Cited by in corpus (5)

• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Quantum-classical distance as a tool to design optimal chiral quantum walk
• Multi-parameter quantum metrology with discrete-time quantum walks
• Coin dimensionality as a resource in quantum metrology involving discrete-time quantum walks
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer