CQIS: Operator algebra and Quantum Information Theory

分析信息是如何在量子系统的状态下编码的，是理解广泛的物理现象的基础，并有可能增强计算、工程和技术中越来越多的应用。在这个项目中，将开发泛函分析、算子代数和量子概率等数学领域的工具，目的是探索与量子信息理论的联系。算符代数理论为量子力学的许多方面提供了一个框架。与量子信息论的概念相结合，算符代数方法可以提供对各种现象的洞察，包括系统的熵、多体系统的性质和黑洞。PI的工作包括与伊利诺伊大学量子研究所IQUIST的合作，是建立一支能够应对量子计算和量子力学无限维方面的新挑战的跨学科努力的一部分。PI将为研究生提供暑期支持，并保持一个多样化的、跨学科的研究小组。PI计划协调一次学习研讨会、新课程设置和其他项目机会(与伊利诺伊几何实验室、IQUIST和芝加哥量子交易所合作)，目标是弥合量子信息科学理论和实践方面的差距。该奖项支持的工作是由量子信息论和算符代数理论中的动力学方面推动的。这一研究将深化目前对von Neumann代数基本性质的理解，提供代数量子场论的计算方面的知识，并为量子信息论中的熵衰变提供强有力的不等式。拟议的算符代数研究成果是高度跨学科的，包括量子电路、多体系统和黑洞面积定律建模的潜在应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Analyzing how information is encoded in the state of a quantum system is fundamental to understanding a wide range of physical phenomena and has the potential to enhance a growing array of applications in computing, engineering, and technology. In this project, tools from the mathematical fields of functional analysis, operator algebras and quantum probability will be developed with the aim of exploring connections to quantum information theory. The theory of operator algebras provides a framework for many aspects of quantum mechanics. Combined with concepts from quantum information theory, operator algebraic methods may provide insight into a variety of phenomena, including the entropy of a system, the properties of many-body systems, and black holes. The work of the PI includes collaboration with IQUIST, a quantum institute at the University of Illinois, and is part of an interdisciplinary effort to build a quantum workforce which can tackle the new challenges of quantum computation and infinite-dimensional aspects of quantum mechanics. The PI will provide summer support for graduate students and maintain a diverse, interdisciplinary research group. The PI plans to coordinate a learning seminar, new course offerings, and other project opportunities (in cooperation with the Illinois Geometry Lab, IQUIST, and Quantum Exchange Chicago) with the goal of bridging the gap between the theoretical and practical aspects of quantum information science. The work supported by this award is motivated by dynamical aspects in quantum information theory and operator algebra theory. This research will simultaneously deepen the current understanding of fundamental properties in von Neumann algebra, provide computational aspects of algebraic quantum field theory and provide powerful inequalities for entropy decay in quantum information theory. The outcomes of the proposed research in operator algebras are highly interdisciplinary, including work on quantum circuits, many-body systems and potential applications on modeling area laws for black holes.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.