NSF Grant for Gene Kopp

Gene KoppLSU Assistant Professor of Mathematics Gene Kopp has recently been awarded a grant from the National Science Foundation (NSF) for a research project that aims to explore the relationship between number theory and quantum information theory. In particular, the project will focus on investigating the connections between Zauner's conjecture, a key problem in quantum information theory, and certain open problems in number theory, including the Stark conjectures.

Zauner's conjecture, which was first proposed in 1999, predicts the existence of highly symmetric and regular geometric configurations known as symmetric informationally complete positive operator-valued measures (SIC-POVMs or SICs). These configurations play a crucial role in quantum information theory, where they are used to describe certain ensembles of quantum measurements. Recent research has revealed an surprising link between SICs and algebraic number theory, supported by robust numerical evidence. However, the mathematical reason for the connection remains unknown.

By bringing together tools and techniques from both number theory and quantum information theory, the research project aims to shed new light on both fields of study. In particular, the project will seek to identify novel connections between SICs and number theory that could lead to significant new insights in both areas.

One of the key practical outcomes of the project will be the development of faster algorithms for computing SICs. This has important applications in quantum state tomography, a technique used to determine the state of a quantum system from measurements, as well as in classical compressed sensing for radar, which involves using a small number of measurements to reconstruct a high-resolution image. Ultimately, the project has the potential to transform our understanding of both number theory and quantum information theory, with broad implications for a wide range of scientific and technological fields.

(Photo: Jolie Cornay)