CQIS: RUI: Quantum State Symmetry and Applications

最近的尖端和不久的将来的量子设备将推动通信，计算和测量中信息处理的边界，从而探索新的物理领域并增强对物理学的基础理解。该项目研究量子纠缠和其他非局域特性，这些特性为这些革命性技术的“量子优势”提供了动力。PI旨在为量子计算机和量子通信网络设计有用的应用程序。除了通过新成果实现科学进步之外，本项目的一个主要组成部分是通过参与真实的研究来培养大学生的科学能力。本项目将实施一个系统框架，研究多体态的局域幺正和置换对称性，以探索多粒子量子纠缠，并开发量子协议的应用。纠缠分析的一个主要工具是使用局域操作群的各向同性子群（即保持给定状态不变的酉集）;这些各向同性群的同构类是纠缠不变量，不仅可以用于分类，还可以用于设计算法和协议。方法论包括李群和李代数理论、表示论和Schur-Weyl对偶，以及申请人过去的成果。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Recent cutting-edge and near-future quantum devices will push the boundaries of information processing in communication, computation, and measurement in ways that will probe new physical realms and enhance the foundational understanding of physics. This project studies quantum entanglement and other nonlocal properties that power the "quantum advantage" of these revolutionary technologies. The PI seeks to design useful applications for quantum computers and quantum communication networks. In addition to achieving scientific progress through new results, a major project component is scientific development of undergraduate students through participation in real research.This project will implement a systematic framework studying local unitary and permutational symmetries of many-body states to probe multiparticle quantum entanglement and to develop applications for quantum protocols. A main tool for entanglement analysis is the use of isotropy subgroups (that is, the set of unitaries that leave a given state invariant) of the group of local operations; the isomorphism classes of these isotropy groups are entanglement invariants that can be used not only for classification, but also for designing algorithms and protocols. Methodology includes the theory of Lie groups and Lie algebras, representation theory and Schur-Weyl duality, together with the proposer's past results.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.