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 means 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.
Scattering as a Quantum Metrology Problem: A Quantum Walk Approach / F. Zatelli, C. Benedetti, M.G.A. Paris. - In: ENTROPY. - ISSN 1099-4300. - 22:11(2020 Nov 19). [10.3390/e22111321]
Scattering as a Quantum Metrology Problem: A Quantum Walk Approach
C. Benedetti
Secondo
;M.G.A. ParisUltimo
2020
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 means 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.File | Dimensione | Formato | |
---|---|---|---|
entropy-22-01321.pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Dimensione
2.72 MB
Formato
Adobe PDF
|
2.72 MB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.