Analysis Student Seminar

Adina Goldberg, Department of Pure Mathematics, University of Waterloo

"Quantum Arrows"

By unearthing extra structure of finite dimensional C*-algebras, we arrive at special symmetric dagger Frobenius algebras (SSFAs). An SSFA has both an algebra and coalgebra structure, and these structures satisfy some additional relationships. When thinking with SSFAs, we can use a diagrammatic tensor notation to depict equations and manipulate maps. I will introduce SSFAs along with this diagrammatic notation, and use them to describe quantum sets and quantum functions, as defined in [1]. At the end, I will mention my current work applying these ideas to build a categorical framework for nonlocal games. Prerequisites: Hilbert spaces, tensor products, some notion of duality.

[1] Musto, Benjamin, David Reutter, and Dominic Verdon. "A compositional approach to quantum functions." Journal of Mathematical Physics 59.8 (2018): 081706.

Zoom Meeting: https://us02web.zoom.us/j/87274747278?pwd=RG1Bak5lbk1GaHdIL0dtSzlBbjdiUT09