RUI: Structure and Local Equivalence of Stabilizers and States

许多新兴的量子信息技术需要访问某种形式的量子纠缠才能运行。理解这些技术需要什么和可能实现什么，由于可能产生大量类型的多粒子纠缠而受挫。多粒子量子纠缠作为一种资源的作用以及随着粒子数量的增加纠缠类型的激增激发了分类程序。一个好的分类方案为理解量子态的性质和它们之间的关系提供了一个框架，将有趣的状态放在一个上下文中，并引入允许解释和解释新发现的概念。本研究的目标是产生这样一种分类方案，并将由此产生的关于量子态结构的知识用于量子计算、通信和密码学中的感兴趣的应用。本项目将提供一个框架和一种语言，用于阐明量子信息处理任务的需求和资源，因此将有助于研究人员努力使这些任务成为现实。该项目的第二个更广泛的影响是对有前途的年轻学生的科学事业的直接影响。本科生将作为研究助理参加，他们将进行计算实验，编写计算机代码以生成示例和测试假设，并证明广泛的假设的特殊情况。从事研究教的知识探究和发现的过程中，课堂工作本身无法实现的方式。该项目将加强黎巴嫩山谷学院的研究环境，支持学生参加研究活动，包括在科学会议上发言和在科学期刊上发表文章。

Many emerging quantum information technologies require access to some form of quantum entanglement in order to operate. Understanding what is needed and what is possible to achieve with these technologies is frustrated by the large number of types of multiparticle entanglement that could be produced. The role of multiparticle quantum entanglement as a resource and the proliferation of entanglement types with increasing particle numbers motivate a program of classification. A good classification scheme provides a framework for understanding properties of and relationships among quantum states, puts interesting states in a context, and introduces concepts that allow explanation and interpretation of new findings. The goals of this research are to produce such a classification scheme, and to use the resulting knowledge about the structure of quantum states in applications of interest in quantum computation, communication, and cryptography.This project will provide a framework and a language in which to articulate the needs and resources of quantum information processing tasks, and will therefore be of use to researchers trying to make these tasks a reality. A second broader impact of this project is direct influence on the scientific careers of promising young students. Undergraduates will participate as research assistants who will carry out computational experiments, write computer code to generate examples and test hypotheses, and prove special cases of broad conjectures. Engagement in research teaches the process of intellectual inquiry and discovery in a way that classroom work alone cannot achieve. This project will strengthen the research environment at Lebanon Valley College by supporting students in research activities including presentations at scientific meetings and publications in scientific journals.