Operational Approach towards Non-Gaussian States - One Photon at a Time

量子纠缠是量子信息处理的关键资源之一，可以在连续变量(CV)系统中以可扩展的方式产生。然而，这种CV纠缠态通常表现为高斯统计，这限制了它们在量子计算中的应用。目前的理论行动的目标是使用量子统计力学的技术来设计和表征实验上可实现的非高斯多模光量子状态。这项任务不仅对量子信息技术的应用是有用的，而且从基础物理的角度来看也是相关的。技术和计算原理必须基于实验上可以获得的量子态。这一行动的重点是应用于多模量子态的光子加法或减法，这在最先进的实验范围内，但在很大程度上没有从理论上进行探索。然而，它为可扩展的应用打开了大门，例如基于测量的量子计算(MBQC)或量子优势测试。这项行动围绕以下研究主题展开：-由光子相加和相减引起的场方图之间的相关性。-光子相加和相减的可实验提取的、拓扑和几何相空间签名。-CV-光子相加和相减量子态中的纠缠。-在基于测量的量子计算和量子至上中的应用。在这些不同主题中开发的工具将数学量子物理与实验量子光学联系起来，以实现行动的主要目标：揭示光子相加和相减高斯态的健壮特性，并最终将这些特性映射到MBQC的资源中。

Quantum entanglement, one of the key resources for quantum information processing, can be generated in a scalable manner in continuous variable (CV) systems. However such CV entangled states typically display Gaussian statistics, which limits their use for quantum computing. The goal of the present theoretical action is to use techniques from quantum statistical mechanics to design and characterise experimentally realisable non-Gaussian multimode quantum states of light. This task is not only useful for applications in quantum information technologies, but is also relevant from a fundamental physics point of view.Technologies and computing principles must be based on experimentally achievable quantum states. The action focuses on photon-addition or -subtraction applied to multimode quantum states, which is within the reach of state of the art experiments but largely unexplored theoretically. Yet, it opens the door to scalable applications, for instance measurement based quantum computing (MBQC) or tests of quantum supremacy. The action is organised around the following research topics: - Correlations between field quadratures induced by photon-addition and -subtraction.- Experimentally extractable, topological and geometric phase space signatures of photon-addition and -subtraction.- CV-entanglement in photon-added and -subtracted quantum states.- Applications in measurement-based quantum computation and quantum supremacy.The tools developed within these different topics connect mathematical quantum physics with experimental quantum optics to achieve the main goal of the action: to uncover robust characteristics of photon-added and -subtracted Gaussian states, and finally to map these properties to resourcefulness for MBQC.