Analysis and Probability seminar

Abstract: In contrast to classical physics, quantum states can be entangled—that is, linked in such a way that measurements performed on one particle are correlated with measurements on another, regardless of the distance between them. This phenomenon, known as Bell nonlocality, gives the appearance that one particle instantaneously influences the other. Previous work has shown that certain correlations can only be produced by preparing a specific entangled state and performing particular measurements.

Self-testing is a framework that aims to identify those correlations that uniquely determine both the quantum state and the measurements used to produce them, up to local isometries. Beyond its significance in Quantum Information Theory, self-testing has played a crucial role in developments in quantum complexity theory and in progress toward resolving Connes’ embedding problem, motivating its study within the context of operator algebras.

In this talk, I will review recent results on self-testing, with a particular focus on how they relate to questions concerning states on tensor products of associated $C^*$ -algebras. This talk is based on joint work with Jason Crann and Ivan G. Todorov.

A large part of the talk will be rather elementary and does not require any deep knowledge of operator algebras.