Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.
Phys Rev Lett. 2014 Jan 31;112(4):040406. doi: 10.1103/PhysRevLett.112.040406.
We show by using statistically rigorous arguments that the technique of weak value amplification does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically, we prove that postselection, a necessary ingredient for weak value amplification, decreases estimation accuracy and, moreover, arranging for anomalously large weak values is a suboptimal strategy. In doing so, we explicitly provide the optimal estimator, which in turn allows us to identify the optimal experimental arrangement to be the one in which all outcomes have equal weak values (all as small as possible) and the initial state of the meter is the maximal eigenvalue of the square of the system observable. Finally, we give precise quantitative conditions for when weak measurement (measurements without postselection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation.
我们通过使用统计学上严格的论证表明，弱值放大技术在单参数估计和信号检测等任务中并不比标准统计技术表现得更好。具体来说，我们证明了后选择（弱值放大的必要成分）会降低估计精度，而且，安排异常大的弱值是一种次优策略。通过这样做，我们明确提供了最优估计器，这反过来又使我们能够确定最优的实验安排，即所有结果都具有相等的弱值（尽可能小），并且计量器的初始状态是系统可观测量的平方的最大本征值。最后，我们给出了精确的定量条件，说明在什么情况下弱测量（没有后选择或异常大的弱值的测量）可以减轻估计中未表征的技术噪声的影响。
