CQIS: Operator algebra and Quantum Information Theory

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

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.