Analysis Seminar

Thursday, March 9, 2023 4:00 pm - 4:00 pm EST

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.


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