We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the length of a uniformly bright incoherent line source with a fixed mid-point and the radius of a uniformly bright incoherent disk shaped source with a fixed center. Prolate spheroidal wavefunctions (PSWFs) on a centered line segment and its generalized version on a centered disk furnish the respective bases for computing the eigenstates and eigenvalues of the one-photon density operator, from which we subsequently calculate QFI with respect to the spatial parameters of the two sources. Zernike polynomials provide a good set into which to project the full source wavefront, and such classical wavefront projection data can realize quantum limited estimation error bound in each case. We subsequently generalize our approach to analyze sources of arbitrary brightness distributions and shapes using a certain class of Bessel Fourier functions that are closely related to the PSWFs. We illustrate the general approach by computing QFI for estimating the lengths of the principal axes of a uniformly bright, centered elliptical disk.
Passive optical superresolution at the quantum limit
University of Oxford（牛津大学）；RTX BBN Technologies（RTX BBN技术公司）；University of Maryland, College Park（马里兰大学帕克分校）；National University of Singapore（新加坡国立大学）；University of Nottingham（诺丁汉大学）；Sorbonne Université（索邦大学）
Quantum limited super-localization and super-resolution of a source pair in three dimensions
最近的一篇论文[Z. Yu和S. Prasad，“Quantum limited superresolution of an incoherent source pair in three dimensions，”arXiv：1805.09227v2 [quant-ph]（2018）]考虑了在所有三维空间中对一对非相干点源的分离矢量进行量子有限估计的问题。在这里，我们扩展我们的分析来处理的问题，同时估计的质心的位置和分离的源对，这相当于本地化两个源同时。我们首先计算同时对质心分离估计的量子费舍尔信息，然后讨论这两个任务之间的基本，估计理论的权衡，我们确认使用模拟。
Quantum-limited estimation of atmospheric turbulence via spatial mode decomposition
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Laboratoire d’Optique Appliqué (LOA), CNRS, École polytechnique, ENSTA, Institut Polytechnique de Paris（巴黎理工学院应用光学实验室（CNRS、巴黎综合理工学院、ENSTA））；Laboratoire Kastler Brossel, Sorbonne Université, ENS-Université PSL, CNRS, Collège de France（索邦大学卡斯勒布罗塞尔实验室（ENS-巴黎文理研究大学、法国国家科学研究中心、法兰西学院））；Department of Theoretical and Mathematical Physics, Kyiv Academic University（基辅学术大学理论与数学物理系）；Department of Mathematics, Kyiv School of Economics（基辅经济学院数学系）
