FET: Small: Establishing an efficient framework for non-Gaussian states engineering and optical implementation of measurements

FET：小型：为非高斯态工程和测量的光学实现建立有效的框架

• 批准号: 2122337
• 负责人: Christos Gagatsos
• 金额: $ 35.76万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2122337&HistoricalAwards=false
• 关键词: FET; Small; Establishing; efficient; framework

Quantum optical technologies (computing, sensing, communications) are fundamentally based on the generation of quantum states and the detection thereof. For example, quantum computing requires reliable generation of the so-called non-Gaussian states in order not to be simulable by a classical computer, while sensing and communications tasks require optical implementation of measurements which might have an abstract mathematical description, e.g., projection on non-Gaussian states. Therefore, non-Gaussianity is a resource which, similar to entanglement, is a cornerstone of quantum information. This project aims to develop a systematic procedure for understanding resource-efficient production of non-Gaussianity and to provide constructive ways of generating any desired non-Gaussian state useful to a plethora of quantum informational tasks. The project also aims to find systematic ways of decomposing any given quantum optical measurement into a set of quantum operations which have known optical implementations. The results that will be enabled by this project are anticipated to have a two-fold impact: advancement of quantum photonic technologies with immediate impact on defense and security systems, and the advancement of basic physics by providing novel mathematical tools for fundamental effects in quantum optics. Graduate students supported by this project will have the opportunity to gain knowledge on continuous variable quantum information systems beyond the Gaussian regime, with an emphasis on non-Gaussianity and entanglement measures. The fundamental results from this project will have far reaching impacts on communications over the future quantum internet, on discovering receiver structures for attaining quantum-limited photonic state discrimination for applications in optical communications and sensing, on the realizability of various near-term applications of photonic quantum processors to problems in optimization, and molecular simulations for evaluating vibronic spectra with applications in drug discovery, and also to special-purpose applications such as all-photonic quantum repeaters based on cluster states for entanglement distribution over long-distances.It is known that Gaussian states and operations -- realizable using squeezed states, lasers and linear optics -- complemented with a single non-Gaussian operation, is "universal", in a sense that any transformation and measurement on a set of optical modes allowed by the laws of quantum physics, can be realized using elements chosen from this aforesaid set. The single non-Gaussian operation could be a non-Gaussian unitary such as a cubic-phase gate. But it can also be a non-Gaussian measurement such as photon resolving (PNR) detection, i.e., projection on Fock states, which have been proven a reliable choice for state engineering in early and recent works. Indeed, one can produce a non-Gaussian state by projecting a subset of a Gaussian state’s modes on the multi-mode Fock basis. However, a systematic way to understand the underlying phenomena, and a neat mathematical description is missing. The broad goals of this project are twofold. First is to devise a mathematical tool, specifically a non-Gaussianity measure, tailored in a fashion that will be useful to state engineering. When the envisioned measure is equal for two different quantum states, the two states must be equal up to a unitary Gaussian operator. This will allow for conclusive results as to if a produced non-Gaussian state is indeed the desired target state (up to a Gaussian unitary operation which is in principle implementable using known photonic components) that a quantum circuit is supposed to be able to produce. Earlier works on non-Gaussianity measures do not possess said property. At the same time earlier works on state engineering focus on fidelity as the measure of closeness of quantum states. Fidelity being close to one is a necessary, but not sufficient criterion for successful state engineering. Finally, the aforesaid tools will enable us to “stitch” together, simple non-Gaussian states, e.g., Fock states, into larger, general entangled non-Gaussian target states desired in a given application. Ultimately, this project aims to devise a systematic way of constructing any desired non-Gaussian state reliably. Our results will be of fundamental interest in a deeper understanding of the mathematical structures of quantum optics, while paving the way to scalable realizations of photonic quantum technologies. Our second goal is to find recipes with which any quantum optical measurement (POVM) can be realized using easy-to-prepare Gaussian states, Gaussian operations and PNR detectors. A POVM on a part of quantum state transforms the initial state into another state from a set of possible states with some probability. Leveraging this property, we will re-write a measurement (e.g., the vacuum-or-not measurement—which has relevance to constructing quantum optimal receivers for laser communications) as an input state (consisting of the state to be measured tensored with ancillary Gaussian states), which undergoes Gaussian unitary evolution, and finally partially projected on Fock states in a manner that gives the proper set of states and probabilities prescribed by the given POVM.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

量子光学技术（计算、传感、通信）基本上基于量子态的产生及其检测。例如，量子计算需要可靠地生成所谓的非高斯状态，以便不被经典计算机模拟，而传感和通信任务需要光学实现测量，其可能具有抽象的数学描述，例如，非高斯状态下的投影。因此，非高斯性是一种资源，类似于纠缠，是量子信息的基石。该项目旨在开发一个系统的程序，用于理解非高斯性的资源有效生产，并提供生成任何所需的非高斯态的建设性方法，这些非高斯态对过多的量子信息任务有用。该项目还旨在找到将任何给定的量子光学测量分解为一组具有已知光学实现的量子操作的系统方法。该项目的成果预计将产生双重影响：量子光子技术的进步对国防和安全系统产生直接影响，以及通过为量子光学中的基本效应提供新的数学工具来促进基础物理学的发展。该项目支持的研究生将有机会获得高斯体系之外的连续变量量子信息系统的知识，重点是非高斯性和纠缠度量。该项目的基本结果将对未来量子互联网上的通信产生深远的影响，对发现用于实现光通信和传感应用中的量子限制光子态鉴别的接收器结构，对光子量子处理器的各种近期应用的可实现性，对优化问题，以及用于评估振动光谱的分子模拟与药物发现，并且还涉及特殊用途的应用，例如基于簇态的全光子量子中继器，用于长时间的纠缠分布，已知的是，高斯状态和操作（可使用压缩状态、激光器和线性光学实现）与单个非高斯操作互补是“通用的”，在某种意义上，量子物理定律所允许的一组光学模式上的任何变换和测量都可以使用从上述组中选择的元件来实现。单个非高斯操作可以是非高斯幺正操作，例如相位门。但它也可以是非高斯测量，例如光子分辨（PNR）检测，即，在早期和最近的工作中，Fock态的投影已被证明是国家工程的可靠选择。实际上，可以通过在多模Fock基础上投影高斯态的模式的子集来产生非高斯态。然而，缺乏一种系统的方法来理解潜在的现象，以及一个简洁的数学描述。该项目的主要目标有两个方面。首先是设计一个数学工具，特别是一个非高斯测量，以一种对国家工程有用的方式量身定制。当两个不同的量子态的所设想的度量相等时，这两个态必须相等，直到一个幺正高斯算子。这将允许关于所产生的非高斯状态是否确实是量子电路应该能够产生的期望目标状态（直到原则上可使用已知光子组件实现的高斯幺正操作）的结论性结果。非高斯测度的早期作品不具有所述性质。与此同时，早期关于状态工程的工作集中在保真度上，作为量子态接近程度的度量。忠诚度接近1是成功的国家工程的必要标准，但不是充分标准。最后，上述工具将使我们能够“缝合”在一起，简单的非高斯状态，例如，Fock态，转换成更大的，一般的纠缠非高斯目标状态在给定的应用中所需的。最终，该项目旨在设计一种系统的方法来可靠地构建任何所需的非高斯状态。我们的研究结果将对更深入地理解量子光学的数学结构具有根本意义，同时为光子量子技术的可扩展实现铺平道路。我们的第二个目标是找到任何量子光学测量（POVM）可以使用容易准备的高斯态，高斯运算和PNR检测器实现的配方。一部分量子态上的POVM将初始态以一定概率从一组可能态中变换到另一个态。利用此属性，我们将重写度量（例如，真空或非真空测量-其与构造用于激光通信的量子最优接收器相关）作为输入状态（由具有辅助高斯态的待测量张量状态组成），其经历高斯幺正演化，最后部分投射到福克州，以给出给定POVM规定的适当的状态和概率集的方式。该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。