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.

订单很重要。在现实生活中，很容易观察到某些操作的顺序大大改变了最终结果。例如，人们可能会想到加热水和添加油。经过近一个世纪的数学家，数学家终于接受了量子力学的挑战，并开发了一种理论，该理论允许研究非交易行动。该项目资助的工作将从字面上采取这一挑战，并从微积分中研究经典的操作，并引入订单依赖时间，时间和时空中执行的所有操作。理论工作的特定应用范围将获得量子信息理论的新见解。量子信息理论修改了香农通过嘈杂的渠道向量子设备发送可靠信息的理论，以期利用“传送”或其他非传统的“怪异行为”。“更具体地说，该提议的工作旨在研究非交流性几何学和非交通性和非交通性和谐分析之间的联系。目的是从非交通性几何形状（例如曲率）中调整一些术语，并表明它用于涉及Laplace和Dirac Operators在非共同空间上的估计。量子信息理论中的工作将针对熵相关的表达式发展不平等，并将其应用于能力，不对称性和平衡时间的概念。该奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子优点和更广泛的影响审查标准通过评估来获得支持。