论文标题
从点过程到量子光学和返回
From point processes to quantum optics and back
论文作者
论文摘要
大约五十年前，在她的开创性博士学位论文中，奥迪尔·麦基（Odile Macchi）引入了永久性和决定性点过程。她最初的动机是为基本骨气或费米子光学实验中的一组检测时间提供模型。经过两十年的安静，这些点过程迅速成为具有非平凡但可拖延的相关结构的点过程的标准示例。特别是，自1990年代以来，确定点过程一直是随机矩阵理论和组合学的技术主力，并且是自2010年代以来机器学习和空间统计数据中排斥点模式的标准模型。同时，我们实验探测骨气和费米子光学中的检测事件之间的相关性的能力已经取得了长足的进展。在这项调查的第一部分中，我们在数学家，物理学家和信号处理者的结合下对Macchi论文及其身体动机的概念进行了现代介绍。我们的目标是为量子光学的点过程的以后的跨学科工作提供共同的知识基础，并重新与永久和确定点过程的物理根源。
Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical experiments, respectively. After two rather quiet decades, these point processes have quickly become standard examples of point processes with nontrivial, yet tractable, correlation structures. In particular, determinantal point processes have been since the 1990s a technical workhorse in random matrix theory and combinatorics, and a standard model for repulsive point patterns in machine learning and spatial statistics since the 2010s. Meanwhile, our ability to experimentally probe the correlations between detection events in bosonic and fermionic optics has progressed tremendously. In Part I of this survey, we provide a modern introduction to the concepts in Macchi's thesis and their physical motivation, under the combined eye of mathematicians, physicists, and signal processers. Our objective is to provide a shared basis of knowledge for later cross-disciplinary work on point processes in quantum optics, and reconnect with the physical roots of permanental and determinantal point processes.
