Applications of algebraic methods in quantum physics

代数方法在量子物理中的应用

• 批准号: 249769-2007
• 负责人: DeGuise, Hubert
• 金额: $ 1.24万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=366086
• 关键词: Applications; algebraic; methods; quantum; physics

This proposal runs along two parallel tracks.  One deals with the construction and properties of quantum mechanical states that have the property of saturating the Heisenberg uncertainty relation.  Such states are called intelligent, and have numerous applications, particularly in optical interferometry.  They also have an important theoretical role in the detection of entanglement, a feature essential to quantum information theory.A second track deals with complementarity in finite dimensional quantum systems.  Here, the objective is to study the construction of sets of states that describe maximally incompatible preparations of a quantum system.  Such states are useful for the optimal implementation of various protocols of quantum information.  The intention is to consider cases, as in a quantum system of dimenion 6, where the dimension is not a prime number or a power of a prime number.  In the latter cases, sets of complementary states are already known and constructed.

这个提议沿着沿着两条轨道进行。一条轨道涉及量子力学状态的构造和性质，这些状态具有饱和海森堡测不准关系的性质。这种状态被称为智能状态，并且具有许多应用，特别是在光学干涉测量中。它们在探测纠缠方面也具有重要的理论作用，这是量子信息理论的一个基本特征。第二条轨道涉及有限维量子系统中的互补性。在这里，目标是研究描述量子系统的最大不相容准备的状态集的构造。这样的状态对于量子信息的各种协议的最佳实现。其目的是考虑在6维量子系统中的情况，其中维数不是素数或素数的幂。在后一种情况下，互补状态的集合已经知道并构造。