权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Operator Algebra Theory in Applications

算子代数理论的应用

基本信息

批准号：
1800872
负责人：
Marius Junge
金额：
$ 27万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-06-01 至 2023-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1800872&HistoricalAwards=false
关键词：
Operator Algebra Theory Applications

项目摘要

Order matters. In real life it is easy to observe that the order of certain operations greatly change the final outcome. As an example one may think of heating water and adding oil. After almost a century mathematicians have finally embraced the challenge from quantum mechanics and developed a theory which allows to study noncommuting operations. The work funded in this project will take this challenge literally and study classical operations from calculus and introduce an order dependence for space, time and all the operations performed in space and time. A particular range of applications of the theoretical work will gain new insights in quantum information theory. Quantum information theory modifies Shannon's theory of sending reliable information through noisy channels to quantum devices in the hope of taking advantage of "teleportation" or other non-traditional "spooky behaviour."More concretely, the proposed work aims to study the connection between noncommutative geometry and noncommutative harmonic analysis. The goal is to adapt some terminology from noncommutative geometry, for example curvature, and show that it an be used for estimates involving Laplace and Dirac operators on noncommutative spaces. The work in quantum information theory will develop inequalities for entropy related expressions and apply them to notions of capacity, asymmetry and time to equilibrium.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.

秩序很重要。在真实的生活中，很容易观察到某些操作的顺序会极大地改变最终的结果。作为一个例子，人们可能会想到加热水和添加油。经过近世纪的数学家们终于接受了来自量子力学的挑战，并发展出一种理论，允许研究非对易操作。该项目资助的工作将从字面上接受这一挑战，并从微积分中研究经典运算，并为空间，时间以及在空间和时间中执行的所有运算引入顺序依赖。理论工作的特定应用范围将在量子信息理论中获得新的见解。量子信息理论修改了香农的理论，即通过嘈杂的信道向量子设备发送可靠的信息，希望利用“隐形传态”或其他非传统的“幽灵行为”。“更具体地说，拟议的工作旨在研究非对易几何和非对易调和分析之间的联系。目标是适应一些术语从非交换几何，例如曲率，并表明它可以用于估计涉及拉普拉斯和狄拉克算子的非交换空间。在量子信息理论方面的工作将发展熵相关表达式的不等式，并将其应用于容量、不对称性和达到平衡的时间等概念。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。