Adina Goldberg: Junior Fellows Seminar: The double category of quantum relations

Speaker
Adina Goldberg, University of Waterloo

Abstract
Enter the world of q-games and q-graphs and look around. (Here, “q-” is shorthand for quantum because it appears repeatedly as a prefix.)
You see the following objects. They look different at first glance…
(1) A q-homomorphism of q-graphs
(2) A synchronous q-strategy for a q-game
(3) A q-subgraph of a q-graph
(4) A perfect q-strategy for a q-game
How much might they have in common?
Building on the work of Weaver, Kornell, and Musto-Reutter-Verdon, we define a new category to answer that question. It’s the double category QRel of q-sets, q-functions, and q-relations. In addition to answering the above question, we illustrate how QRel suggests, distinguishes, and motivates quantizations of some constructions/results from classical graph theory and traditional nonlocal games.