Title: The mathematics of quantum functionality certification

Abstract:

In this talk, I will introduce the concept of self-testing, which aims to address the fundamental question of how to certify the proper functioning of black-box quantum devices. Self-testing represents the strongest form of quantum functionality certification, enabling a classical user to infer the quantum state and measurements used to produce the observed measurement statistics. Despite its operational definition, in fact self-testing is closely tied to understanding irreducible representations of groups and algebras along with their stability properties. I will survey key self-testing results and discuss outstanding questions in the field.