近日，中国科学技术大学庞盛世团队研究了二维非相干光源间全距离最佳量子超分辨率。该研究于2026年3月9日发表在《物理评论A》杂志上。
瑞利准则长期以来被视为光学成像分辨率的基本极限。多参数量子计量学的最新进展催生了能够突破该极限的量子超分辨技术，使得在估计两个邻近非相干点源间距时仍能保持非零精度。对于二维光学系统，目前已有针对非相干点源笛卡尔坐标分量的量子超分辨研究，但两点源间完整距离的估计精度极限迄今尚未明确。
研究组探讨了二维成像系统中任意强度非相干点源间完整距离的估计精度问题。通过多参数量子估计理论，他们推导了距离估计的终极精度极限，并证明当间距趋近于零时该精度仍保持非零值，从而超越瑞利准则。进一步研究表明，两点源相对取向会影响估计精度——当点扩散函数非圆对称时，通过将点源沿特定方向排列可提升测量精度，其增强幅度取决于点扩散函数偏离圆对称的程度。最后，研究组以高斯型点扩散函数的非相干光源为例对研究结果进行了验证。
附：英文原文
Title: Optimal quantum superresolution for full distance between incoherent optical sources in two dimensions
Author: Junyan Li, Shengshi Pang
Issue&Volume: 2026/03/09
Abstract: The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing precision in estimating the separation between a pair of closely located incoherent point sources. For two-dimensional optical systems, the quantum superresolution has been studied for the Cartesian components of separation between two incoherent point sources. However, the precision limit of estimating the full distance between two point sources remains unknown so far. In this paper, we investigate the estimation precision of the full distance between two incoherent point sources with arbitrary intensities in a two-dimensional imaging system. Through the multiparameter quantum estimation theory, we obtain the ultimate estimation precision for the distance and show that it remains nonzero when the distance approaches zero, which surpasses the Rayleigh criterion. We further show the dependence of the estimation precision on the relative orientation between the two point sources, which leads to a scheme that can enhance the precision by aligning the sources along proper directions if the point-spread functions are not circularly symmetric, and the enhancement is determined by the extent to which the point-spread functions deviate from circular symmetry. Finally, the results are illustrated by incoherent sources with Gaussian point-spread functions.
DOI: 10.1103/tzyy-cwb4
Source: https://journals.aps.org/pra/abstract/10.1103/tzyy-cwb4