Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA.
Phys Rev Lett. 2015 Sep 18;115(12):120401. doi: 10.1103/PhysRevLett.115.120401. Epub 2015 Sep 15.
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.
后选择弱测量是一种用于放大弱物理效应的有用协议。然而，最近关于它是否在精度上有优势存在争议。虽然现在已经清楚地表明，保留失败的后选择可以比丢弃它们产生更多的 Fisher 信息，但后选择测量本身的优势仍然需要澄清。在这封信中，我们通过分别研究两种广泛使用的估计策略来解决这个问题：平均测量结果和最大似然估计。对于第一种策略，我们发现了一个令人惊讶的结果，即指针的压缩相干态可以使后选择的弱测量比标准弱测量具有更高的信噪比，而所有标准相干态都不能，这表明通过后选择提高弱测量的精度需要在指针状态中存在“非经典性”。对于第二种策略，我们表明，即使不使用失败的后选择事件，后选择弱测量的量子 Fisher 信息通常也大于标准弱测量的量子 Fisher 信息，但可以通过选择适当的系统状态来缩小差距。
