Zatelli Francesco, Benedetti Claudia, Paris Matteo G A
Dipartimento di Fisica 'Aldo Pontremoli', Università degli Studi di Milano, I-20133 Milano, Italy.
INFN, Sezione di Milano, I-20133 Milano, Italy.
Entropy (Basel). 2020 Nov 19;22(11):1321. doi: 10.3390/e22111321.
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.
我们研究了量子粒子在一组离散位置上被一维势垒散射的问题。我们将该问题形式化为在具有杂质的晶格上的连续时间量子行走，并使用量子费希尔信息作为量化势垒高度估计中最大可能精度的一种手段。我们引入了行走者的合适初始状态，并推导了散射态的反射和透射概率。我们表明，虽然量子费希尔信息受初始波包的宽度和中心动量影响，但这种依赖性对量子信噪比来说较弱。我们还表明，二分位置测量提供了一种近乎最优的检测方案。
