Yuming Zhao, Department of Pure Mathematics, University of Waterloo
"An operator algebraic formulation of self-testing"
Suppose we have a physical system consisting of two separate labs, each capable of making a number of different measurements. If the two labs are entangled, then the measurement outcomes can be correlated in surprising ways. In quantum mechanics, we model physical systems like this with a state vector and measurement operators. However, we do not directly see the state vector and measurement operators, only the resulting measurement statistics (which are referred to as a "correlation"). There are typically many different models achieving a given correlation. Hence it is a remarkable fact that some correlations have a unique quantum model. A correlation with this property is called a self-test.
In this talk, I'll introduce the standard definition of self-testing, discuss its achievements as well as limitations, and propose an operator algebraic formulation of self-testing in terms of states on C*-algebras. This new formulation captures the standard one and extends naturally to commuting operator models. I'll also discuss some related problems in operator algebras.
Based on arXiv:2301.11291, joint work with Connor Paddock, William Slofstra, and Yangchen Zhou.