论文标题
超过两个点源的量子极限的超分辨率
Superresolution at the quantum limit beyond two point sources
论文作者
论文摘要
超分辨率是指超出标准经典技术（例如直接检测）的精度的图像参数的估计。在Lu等人的开创性工作中，证明了两个点源（带有已知质心）的分离距离的测量值以实现量子cramer-rao结合。这项工作暗示了来源的反射对称性。在这里，我们提出了一个框架，该框架在星座中使用更通用的对称性来构建量子测量，该量子测量在参数的估计中实现了量子cramer-rao。我们展示了如何使用该技术在具有两个以上源的对称点源星座中同时估计参数。为了显式使用对称性，我们可以在保持这种对称性的动量空间中使用离散点扩展功能。该框架使我们能够使用量子计算中的技术，例如傅立叶变换和线性光电电路来实现最佳测量。据我们所知，这是第一部作品，它显示了超过两个点源的估计和模态转换量的量子限制。
Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point sources (with a known centroid) was shown to achieve the quantum Cramer-Rao bound. This work made implicit use of reflection symmetry of the sources. Here we present a framework that uses more general symmetry in a constellation to construct a quantum measurement that achieves the quantum Cramer-Rao bound in estimation of parameters. We show how this technique can be used to estimate parameters simultaneously in symmetric point-source constellations with more than two point sources. In order to use symmetry explicitly, we make use discrete point spread functions in momentum space that maintain this symmetry. This framework allows us to use techniques from quantum computing such as Fourier transforms and linear optical circuits to implement the optimal measurement. To our knowledge, this is first work that shows for more than two point sources achievable quantum limits of estimation and modal transformations.
