Q+ Hangout: Tobias Fritz (Perimeter Institute)

We'd like to announce the next Q+ hangout.  As usual, if you are watching with a group and want to reserve a seat in the hangout then leave a comment on the event page.  Everyone else can watch on the livestream.

Title: A Combinatorial Approach to Nonlocality and Contextuality

Abstract:
Most work on contextuality so far has focused on specific examples and concrete proofs of the Kochen-Specker theorem, while general definitions and theorems about contextuality are sparse. For example, it is commonly believed that nonlocality is a special case of contextuality, but what exactly does this mean? After a brief discussion of previous work, I will introduce our "device-independent" approach to contextuality based on the mathematics of test spaces and explain how nonlocality is indeed a special case of contextuality. This work builds on the graph-theoretic approach of Cabello, Severini and Winter by improving on several of its shortcomings and merging it with the work of Foulis and Randall on test spaces. Our results include:

(1) various relationships to graph invariants, similar to CSW;
(2) a proof that our set of quantum models *cannot* be characterized by a graph invariant;
(3) a proof that the set of all models satisfying the Consistent Exclusivity principle at any number of copies is not convex;
(4) new results on the Shannon capacity of graphs;
(5) an "inverse sandwich conjecture" with ramifications for C*-algebra theory and quantum logic.