标题： 通过连续时间位置测量监测波函数 显示英文标题

标题： Monitoring the wave function by time continuous position measurement

摘要： 我们考虑一个量子粒子在势场中运动的单个副本，并证明通过仅连续测量其位置，可以监测其完整的波函数。虽然我们假设势场是已知的，但初始状态下关于粒子的状态没有任何信息。 为了监测波函数，根据势场的影响传播波函数的一个估计值，并根据位置测量的结果不断更新该估计值。通过数值模拟，我们证明了对于所研究的势场，在有限的时间内，这种估计可以达到低于100%的任意精度。 通过这种方法，在测量开始后的一段时间内，可以获得状态演化的精确实时记录，其中包括连续测量的影响。此外，只要突然扰动（例如来自环境粒子的随机动量冲击）不发生得太频繁，该方法对这些扰动具有一定的鲁棒性。 显示英文摘要

摘要： We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no information is available about its state initially. In order to monitor the wave function, an estimate of the wave function is propagated due to the influence of the potential and continuously updated according to the results of the position measurement. We demonstrate by numerical simulations that the estimation reaches arbitrary values of accuracy below 100 percent within a finite time period for the potentials we study. In this way our method grants, a certain time after the beginning of the measurement, an accurate real-time record of the state evolution including the influence of the continuous measurement. Moreover, it is robust against sudden perturbations of the system as for example random momentum kicks from environmental particles, provided they occur not too frequently.