Homotopical approach to magic assignments

Cihan Okay (University of British Columbia), Robert Raussendorf (University of British Columbia)

We extend Arkhipov’s graph theoretic characterization of magic assignments to arbitrary collection of contexts by relaxing the require-ment that each observable belongs to exactly two contexts. We intro-duce topological realizations of operator constraints by 2-dimensional 
cell complexes. Then we prove that the assignment is non-magic if the first homotopy group of the topological realization is trivial.