Certification of Quantum Devices via Operator-Algebraic Techniques

Explore the concept of self-testing in quantum devices through this 50-minute semi-plenary talk by Laura Mancinska from the University of Copenhagen. Delve into operator-algebraic techniques and their application in certifying the proper functioning of black-box quantum devices. Discover the close link between self-testing and stability of algebraic relations, and learn about a family of protocols capable of certifying quantum states and measurements of arbitrarily large dimension using just four binary-outcome measurements. Examine the algebraic analogue of the Gowers-Hatami stability theorem for group representations, which serves as a key proof ingredient. Follow the talk's structure, covering topics such as robust self-testing, quantum strategies derived from projections, and the implications of the main results presented.

Intro
How do we verify proper functioning of a quantum device?
Self-testing in a nutshell
Robust self-testing: formal definition
What can be self-tested and how efficiently?
Projections adding up to scalar times the identity
Quantum strategy from projections summing up to scalar times the identity
Proof sketch: Outline
Proof sketch: Approximate representations
Summary: Main result and implications