CQIS: Operator algebra and Quantum Information Theory

分析信息如何在量子系统状态下编码是理解广泛物理现象的基础，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。结合量子信息理论的概念，算子代数方法可以提供对各种现象的洞察，包括系统的熵，多体系统的属性和黑洞。 PI的工作包括与伊利诺伊大学量子研究所IQUIST的合作，并且是建立量子劳动力的跨学科努力的一部分，该劳动力可以应对量子计算和量子力学无限维方面的新挑战。 PI将为研究生提供夏季支持，并维持一个多元化的跨学科研究小组。 PI计划协调学习研讨会，新课程和其他项目机会（与伊利诺伊州几何实验室，IQUIST和量子交换芝加哥合作），目标是弥合量子信息科学理论和实践方面之间的差距。 该奖项支持的工作是由量子信息理论和算子代数理论的动力学方面的动机。 这项研究将同时加深目前对冯诺依曼代数基本性质的理解，提供代数量子场论的计算方面，并提供量子信息理论中熵衰减的强大不等式。在算子代数的拟议研究成果是高度跨学科的，包括量子电路，多体系统和模拟面积定律的黑洞的潜在应用的工作。这个奖项反映了NSF的法定使命，并已被认为是值得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的支持。

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.