Institute for Theoretical Physics, Vienna University of Technology (TU Wien), 1040 Vienna, Austria.
Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France.
Phys Rev Lett. 2021 Dec 3;127(23):233201. doi: 10.1103/PhysRevLett.127.233201.
Determining the ultimate precision limit for measurements on a subwavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle's properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle's position within its nonabsorbing environment. This invariance law breaks down only in the regime of Anderson localization, due to increased C_{0}-speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.
用相干激光测量亚波长粒子的极限精度是一个目标，其应用领域包括生物物理学和纳米技术等。在这里，我们证明了在粒子周围设置复杂的散射环境平均来说不会对与粒子测量相关的平均量子 Fisher 信息产生任何影响。作为一个显著的结果，当估计粒子的性质时，在弹道和扩散散射区域中可以达到的平均精度是相同的，而与粒子在非吸收环境中的位置无关。由于 C_0-斑点相关性的增加，只有在安德森局域化的情况下，这种不变性定律才会失效。最后，我们展示了这些结果如何与通过空间优化输入场实现的平均量子 Fisher 信息相关联。
