Property testing is a fundamental subject in theoretical computer science and combinatorics, which studies when and how global properties of large objects (such as a massive data set or a huge graph) can be robustly inferred when given only local views of the object. Famous examples of property testing include testing whether a given graph is triangle-free or whether a given boolean function is linear.

In this talk, I'll present a generalization of the property testing model where the "local views" of an object are not given by deterministic evaluations, but instead by the probabilistic outcomes of measurements on a quantum state. This gives rise to a noncommutative model of property testing, and raises many interesting questions at the interface of complexity theory, quantum information, operator algebras, and more. Finally, I'll describe how the recent quantum complexity result MIP* = RE can be viewed through the lens of noncommutative property testing.