量子物理中的压缩传感理论及其应用

Recent years, the newly developed compressed sensing (CS) theory is a breakthrough in physical measurements including signal and image processing. It has been successfully applied in many fields, and the processing efficiency of physical measurements has improved much more while the image resolution has beyond the traditional limit. If the traditional Shanno/Nyquist sampling theorem needs to samplings N, the C-S theory proves that the requirement samplings to reconstruct the original (sparse) signal are only LogN with the random low sampling and the most optimized process. CS has been become hot spots, but mainly is limited to the classical non-coherent signals, and it just started in the application of quantum physics. Based on our previous studies on the relation between L1-norm and quantum thoery, reconstruction of digital inline holography with CS, CS theory in the relation of Wigner function and wave function, and CS in the single photon counting imaging system, we will intend to promote CS theory into the application of quantum physics in this project. We will systematically research on the description of the quantum state, physical measurements, as well as super-resolution studies. We try to develop a more effective way of CS theory to describe the quantum system, and to calculate the expected value of the complex process of physical quantities. Combined with the application of CS in the single photon counting imaging technology, we will study the quantum effects in the condition of extremely low illumination of the photon imaging. We try to develop the CS theory into a quantum applied theory under the basement of quantum theory, and provide some new ideas and new methods for the study of quantum physics. This project is a hot research topic in the international forefront of cross-cutting areas, which is involved many cross subjects, such as math, physics, and information. It is quite high difficult, a broad knowledge involved, strong exploratory, and potential significant both in theory and application. the application of CS in the quantum system. It is possible to bring quantum physics into a new and higher field.

近年来迅速发展的新型压缩传感(CS)理论是在物理测量（包括信号和图像）处理方面的一个突破性进展，已经在很多方面得到成功应用，使信号和图像处理效率得到极大提高，突破了传统方法的理论极限。目前CS理论已在国际上形成研究热点，但主要限于经典非相干信号，在量子物理中的应用刚刚起步。本课题在我们对L1 范数与量子理论的关联性、CS理论在Wigner函数与波函数对应关系和CS单光子计数成像技术研究的基础上，拟将该理论推广到量子物理应用研究中，开展对量子态的描述、物理量测量、以及超分辨研究等，把CS发展成在量子理论基础上的量子应用理论。从理论上探求CS在量子系统的应用，研究极弱光下光子成像的量子效应，提供一些新思路和新方法。本项目是国际前沿交叉领域的热点研究课题，涉及数学、物理、信息等多个交叉学科，难度大，涉及面宽，探索性强，在理论和应用两方面均有重要意义，有可能将量子物理的研究引入一个新的更高的领域。

近年来迅速发展的新型压缩传感(CS)理论是在物理测量（包括信号和图像）处理方面的一个突破性进展，已经在很多方面得到成功应用，使信号和图像处理效率得到极大提高，突破了传统方法的理论极限。目前CS理论已在国际上形成研究热点，但主要限于经典非相干信号，在量子物理中的应用刚刚起步。本课题在我们对L1 范数与量子理论的关联性、CS理论在Wigner函数与波函数对应关系和CS单光子计数成像技术研究的基础上，将该理论推广到量子物理应用研究中，开展了对ＣＳ在量子态层析和多比特量子系统密度矩阵的计算，把CS发展成在量子理论基础上的量子应用理论。从理论和实验上研究了CS在量子系统的应用，研究了极弱光下光子成像的量子效应。研究结果表明，ＣＳ的引入不但减少了重建所需的存储空间已经重建时间，同时减少了重建过程所需要的采样次数，计算时间的问题等，而且保持重建密度矩阵的精度不变。