论文标题
量子步行：第一个检测到的过渡时间
Quantum walks: the first detected transition time
论文作者
论文摘要
我们考虑在重复的投影测量值下以固定速率$ 1/τ$在图形上演变的粒子在图上演变的量子第一检测问题。在有限维的希尔伯特空间中获得了平均第一个检测到的过渡时间的一般公式，其中沃克的初始状态$ |ψ_{\ rm in} \ rangle $与检测到的状态$ | |ψ_{\ rm d} \ rangle $。我们专注于分歧的平均过渡时间，其中总检测概率通过将问题映射到位于单位磁盘上的经典电荷的场理论中，表现出其值的不连续下降。接近模型的临界参数，该模型表现出平均过渡时间的爆炸，我们在平均过渡时间中获得了简单的表达式。 Using previous results on the fluctuations of the return time, corresponding to $|ψ_{\rm in}\rangle = |ψ_{\rm d}\rangle$, we find close to these critical parameters that the mean transition time is proportional to the fluctuations of the return time, an expression reminiscent of the Einstein relation.
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/τ$. A general formula for the mean first detected transition time is obtained for a quantum walk in a finite-dimensional Hilbert space where the initial state $|ψ_{\rm in}\rangle$ of the walker is orthogonal to the detected state $|ψ_{\rm d}\rangle$. We focus on diverging mean transition times, where the total detection probability exhibits a discontinuous drop of its value, by mapping the problem onto a theory of fields of classical charges located on the unit disk. Close to the critical parameter of the model, which exhibits a blow-up of the mean transition time, we get simple expressions for the mean transition time. Using previous results on the fluctuations of the return time, corresponding to $|ψ_{\rm in}\rangle = |ψ_{\rm d}\rangle$, we find close to these critical parameters that the mean transition time is proportional to the fluctuations of the return time, an expression reminiscent of the Einstein relation.
