论文标题
弱值扩大分析超出了弱测量的AAV极限
Weak-value-amplification analysis beyond the AAV limit of weak measurements
论文作者
论文摘要
Aharonov，Albert和Vaidman（AAV）提出的弱价值（WV）测量引起了与量子计量学的联系。在这项工作中，我们将分析扩展到AAV限制之外，并获得一些主要结果。 （i）我们获得信噪比（SNR）的非扰动结果。与AAV的预测相反，我们发现当AAV的WV $ A_W $变大，即，在$ G | A_W |^2 >> 1 $中，SNR渐近差，其中$ g $是测量强度。 （ii）随着$ g $（但也很小）的增加，我们发现SNR与AAV限制下的结果相当，而两者都可以达到 - 实际上前者可能会略微超过标准测量的SNR。但是，随着$ g $的进一步增加，尽管提高了选择后的概率，但WV技术的效率将比标准测量效率降低。 （iii）我们发现，Fisher信息可以定性地表征估计精度，但随着$ G $的增加，它们的差异将变得更加突出。 （iv）我们在存在技术噪声的情况下对SNR进行分析表达式，并说明了假想WV测量的特殊优势。 SNR的非扰动结果表现出有利的噪声强度范围，并允许最佳测定。
The weak-value (WV) measurement proposed by Aharonov, Albert and Vaidman (AAV) has attracted a great deal of interest in connection with quantum metrology. In this work, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain non-perturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV's prediction, we find that the SNR asymptotically gets worse when the AAV's WV $A_w$ becomes large, i.e., in the case $g|A_w|^2>>1$, where $g$ is the measurement strength. (ii) With the increase of $g$ (but also small), we find that the SNR is comparable to the result under the AAV limit, while both can reach -- actually the former can slightly exceed -- the SNR of the standard measurement. However, along a further increase of $g$, the WV technique will become less efficient than the standard measurement, despite that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet their difference will become more prominent with the increase of $g$. (iv) We carry out analytic expressions of the SNR in the presence of technical noises and illustrate the particular advantage of the imaginary WV measurement. The non-perturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.
