You are cordially invited to the Quantum Computing Seminar organized by the Department of Mathematics.
Speaker: Walker H. Stern (Bilkent University)
“Higher quantum theory and 2-Hilbert spaces”
Abstract: In this talk, we will discuss categorifications of Hilbert spaces, called $emph{2-Hilbert spaces}$. In much the same way as Hilbert spaces are sets with linear structures and inner products satisfying a completeness condition, 2-Hilbert spaces are categories with linear structures and inner products on their hom-sets, satisfying a categorical completeness condition. We will develop the monoidal bicategory of 2-Hilbert spaces, and discuss how teleportation and quantum dense coding manifest in this framework.
References:
1. Heunen, Chris, and Jamie Vicary. Categories for Quantum Theory: an introduction. Oxford University Press, 2019. Chapter 8
2. Baez, John. Higher-dimensional algebra II: 2-Hilbert spaces. Advances in Mathematics, 127(2):125–189, 1997. Chapters 1-4
3. Bartlett, Bruce. On unitary 2-representations of finite groups and topological quantum field theory.
arXiv:0901.3975. Sections 3.1, 3.2, & 3.3.
Date: Friday, May 17, 2024
Time: 14:00
Place: SA141 – Mathematics Seminar Room & ZOOM
To request the event link, please send a message to selman.ipek@bilkent.edu.tr