Invariant Theory in Quantum Information

When

November 1, 2024 | 3:30 p.m. – 4:30 p.m.
Refreshments provided

Where

University Hall 4002

Speaker

Luke Oeding

Abstract

Entanglement is a resource that is utilized on quantum devices to cary information on quantum bits (qubits), and is what gives a quantum computer its theoretical advantage over its classical counterpart. Invariant theory and quantum mechanics have always been linked. Roughly speaking, representations of groups govern quantum states. Since quantum information is concerning multii-particle states, tensors (or hypermatrices) are the natural mathematical objects, and the invariant theory of tensors governs entanglement types for n-qubit systems. My collaborators have been investigating new types of tensor decompositions, such as a version of the Jordan decomposition as well as new versions of the higher order singular value decomposition and their connections to quantum information.

I will start from a basic level and explain the central mathematical objects, tensors, their symmetries, and how we utilize invariant theory to study entanglement types. This is joint work with Frederic Holweck (UTBM), Hamza Jaffali (ColibriTD), and Ian Tan (Auburn).

The talk will be focused on and accessible to graduate students. All are encouraged to attend.