The theory of C*-algebras, which originated in the 1930s in the study of quantum mechanics, is now a vital part of modern mathematical analysis, with applications across the mathematical sciences. C*-algebras arise naturally in connection with a variety of mathematical objects of interest, including groups, dynamical systems, and discrete graphs. This project concerns the structure and properties of C*-algebras associated to quantum graphs. A relatively recent generalization of the classical notion of a discrete graph, quantum graphs have proven to be useful in quantum information theory: just as classical discrete graphs encode confusion due to noise in a classical communication channel, quantum graphs encode confusion due to noise in a quantum channel. The project will generate new methods for analyzing the structure of quantum Cuntz-Krieger algebras and their underlying quantum graphs, and explore their interplay with quantum information theory, a topic of growing global interest. Educational opportunities for undergraduates will be provided through research projects, and a new, interdisciplinary certification program in introductory quantum information theory at the PI’s home institution. Student researchers and visiting speakers will be recruited with a focus on diversity and representation. Given a simple discrete graph, the Cuntz–Krieger algebra for the graph is a universal C*-algebra which encodes the graph’s edge relations. The Kubo-Martin-Schwinger (KMS) st