Weak-value-amplification analysis beyond the Aharonov-Albert-Vaidman limit
Weak-value-amplification analysis beyond the Aharonov-Albert-Vaidman limit
复制标题
超出 Aharonov-Albert-Vaidman 极限的弱值放大分析
DOI：
10.1103/physreva.102.042601
复制
发表时间：
2020-10-01
影响因子：
2.9
通讯作者：
Li, Xin-Qi
中科院分区：
文献类型：
--
作者：
Ren, Jianhua;Qin, Lupei;Li, Xin-Qi
由Aharonov、Albert和Vaidman提出的弱值(WV)测量在量子计量学领域引起了人们极大的兴趣。在本文中，我们超越了AAV的限制，得到了几个主要的结果。(I)我们得到了信噪比(SNR)的一个非扰动结果。与AAV预测相反，我们发现当AAV WV${A}_{w}$变大时，即在$g|{A}_{w}{|}^{2}\ensuremath{\gg}1$的情况下，SNR渐近地变差，其中$g$是测量强度。(Ii)随着$g$的增加(但也很小)，我们发现SNR与AAV限制下的结果相当，但两者都可以达到-实际上前者可以略高于-标准测量的SNR。然而，随着$g$的进一步增加，WV技术的效率将变得低于标准测量，尽管选择后概率增加了。(3)我们发现Fisher信息可以和SNR一样定性地表征估计精度，但这种差异会随着$g$的增加而变得更加显著。(4)给出了在存在技术噪声的情况下信噪比的解析表达式，并说明了虚WV测量的独特优势。信噪比的非扰动结果显示了噪声强度的有利范围，并允许进行最优确定。
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 paper, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain a nonperturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV prediction, we find that the SNR asymptotically gets worse when the AAV WV ${A}_{w}$ becomes large, i.e., in the case $g|{A}_{w}{|}^{2}\ensuremath{\gg}1$, 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, with a further increase of $g$, the WV technique will become less efficient than the standard measurement, despite the fact that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet the 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 nonperturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.