【报告摘要】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 will introduce an operator-algebraic formulation of self-testing in terms of states on C*-algebras. Many nonlocal games of interest, including XOR games and synchronous games, have a "nice" game algebra in the sense that optimal/perfect strategies correspond to tracial states on the game algebra. For these nonlocal games, I will show how self-testing is related to the uniqueness of tracial states on the game algebras. I will also discuss connections between the stability of game algebras and the robustness of self-tests.