RUI: Space of Multiparticle Entanglement Types

RUI：多粒子纠缠类型的空间

• 批准号: 0555506
• 负责人: Scott Walck
• 金额: $ 16万
• 依托单位: Lebanon Valley College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0555506&HistoricalAwards=false
• 关键词: RUI; Space; Multiparticle; Entanglement; Types

Classification of entanglement types and describing the set of states whichshare a given entanglement type for quantum systems whose subsystems arequantum bits (qubits) is an important open problem in the field of quantuminformation theory. Its importance derives from applications including quantumcomputation algorithms and quantum communications protocols whichrely on entanglement as an essential resource.Most known results utilize polynomial invariants (polynomial functions ofstate vector coefficients) to analyze entanglement. The complexity of thisapproach grows exponentially with the number of qubits and thus far hasproved impractical to apply to systems with more than a small number ofqubits.An alternative approach using geometric invariants based on the Lie algebra of the group of local unitary transformations will be explored. In contrast to polynomial invariants, this is applicable to systems with an arbitrary number of qubits. The PIs have achieved general results that distinguish products of singletstates as having a unique extremal property among entanglement types.The PIs propose to further develop this machinery to refine existing invariants,to construct new invariants, and to prove a number of conjectures includingentanglement classification statements about product states and n-cat states.

量子系统的纠缠类型的分类和描述子系统为量子比特（quantum bits）的量子系统共享给定纠缠类型的态集是量子信息论领域的一个重要的开放问题。它的重要性来自于量子计算算法和量子通信协议等依赖于纠缠作为一种基本资源的应用，大多数已知的结果利用多项式不变量（状态向量系数的多项式函数）来分析纠缠.这种方法的复杂性随着量子比特的数量呈指数增长，到目前为止，已经证明应用于具有多于少量量子比特的系统是不切实际的。将探索基于局部酉变换群的李代数的使用几何不变量的替代方法。与多项式不变量相反，这适用于具有任意数量量子比特的系统。PI已经取得了一般性的结果，区分产品的单态作为一个独特的极端属性之间的纠缠类型PI建议进一步发展这一机制，以改善现有的不变量，构造新的不变量，并证明了一些包括纠缠分类声明的产品状态和n-cat状态。