Quantum Entanglement and Separability

这项研究是在与量子计算和量子信息理论的量子力学基础相关的数学模型的背景下进行的。 该项目的重点是量子纠缠的量化和表征，这是量子力学计算模型与经典模型的关键区别。 该研究的主要主题是利用模型的固有几何结构来对不同类型的纠缠进行分类和量化，为检测纠缠量子态提供标准，并激发和改进用于量子信息理论研究的新数学技术。计算机组件尺寸的不断减小必然导致对量子力学效应的考虑，并且可能，发展出一种能解决目前技术无法解决的问题的计算机。 发展所需技术的一个重要方面是在实验室中探测和测量光子纠缠态。 该项目的一个关键目标是将数学理论直接与检测这种纠缠的实验室协议的设计联系起来。 此外，对纠缠本质的更深入了解将为量子计算和量子通信问题提供新的实验和不同的方法。

This research is set in the context of mathematical models related to the quantum mechanical foundations of quantum computing and quantum information theory. The project focuses on the quantification and characterization of entanglement, the key property distinguishing the quantum mechanical model of computation from the classical model. The major theme of the research is to exploit the inherent geometry of the model in order to classify and quantify different kinds of entanglement, to provide criteria for the detection of entangled quantum states, and to motivate and refine new mathematical techniques for the study of quantum information theory.Continued reduction of the size of components in computers necessarily leads to a consideration of quantum mechanical effects and, potentially, to the development of a computer that can solve problems inaccessible to current technology. An important aspect of developing the required technology is the detection and measurement of putatively entangled states in the laboratory. A key goal of this project is to relate the mathematical theory directly to the design of laboratory protocols for the detection of such entanglement. In addition, greater insight into the nature of entanglement will suggest both new experiments and different approaches to issues of quantum computation and quantum communication.