Ni Zhenbo, Zheng Yujun
School of Physics, Shandong University, Jinan 250100, China.
Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel.
Entropy (Basel). 2023 Aug 18;25(8):1231. doi: 10.3390/e25081231.
We consider the first detection problem for a one-dimensional quantum walk with repeated local measurements. Employing the stroboscopic projective measurement protocol and the renewal equation, we study the effect of tunneling on the detection time. Specifically, we study the continuous-time quantum walk on an infinite tight-binding lattice for two typical situations with physical reality. The first is the case of a quantum walk in the absence of tunneling with a Gaussian initial state. The second is the case where a barrier is added to the system. It is shown that the transition of the decay behavior of the first detection probability can be observed by modifying the initial condition, and in the presence of a tunneling barrier, the particle can be detected earlier than the impurity-free lattice. This suggests that the evolution of the walker is expedited when it tunnels through the barrier under repeated measurement. The first detection tunneling time is introduced to investigate the tunneling time of the quantum walk. In addition, we analyze the critical transitive point by deriving an asymptotic formula.
我们考虑具有重复局部测量的一维量子行走的首次探测问题。采用频闪投影测量协议和更新方程，我们研究隧穿对探测时间的影响。具体而言，我们研究在无限紧束缚晶格上的连续时间量子行走的两种具有物理实际意义的典型情况。第一种是不存在隧穿且具有高斯初始态的量子行走情形。第二种是在系统中添加一个势垒的情形。结果表明，通过改变初始条件可以观察到首次探测概率衰减行为的转变，并且在存在隧穿势垒的情况下，粒子比无杂质晶格能更早被探测到。这表明在重复测量下，当行走者隧穿势垒时其演化会加快。引入首次探测隧穿时间来研究量子行走的隧穿时间。此外，我们通过推导渐近公式来分析临界转移点。
