Q+ Hangout: Tobias Fritz

Here are the details of the next Q+ hangout. To watch live, visit the event page at the appointed hour. Be aware of the fact that although North America has switched to DST, the UK has not yet and the time is still listed in GMT/UTC.

Date/time: Tuesday 25th March 2014 2pm GMT/UTC

Speaker: Tobias Fritz (Perimeter Institute)

Title: A Combinatorial Approach to Nonlocality and Contextuality

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.

This talk is based on arXiv:1212.4084.

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