Hybrid quantum teleportation, subfactors and quantum chromatic numbers

Jason Crann (Carleton University)

Monday 10th October 10:00-11:00 Maths 311B


Motivated by recent activity in hybrid quantum error correction and the theory of local quantum operations, we generalize Werner’s teleportation schemes to the commuting operator framework.  For a large class of inclusions N \subset M of finite von Neumann algebras, we obtain a correspondence between “tight” teleportation schemes for the relative commutant N’ \cap M and unitary Pimsner-Popa bases for M over N. When N is homogeneous and M is a finite-dimensional factor, we build on work of Brannan-Eifler-Voigt-Weber and establish an analogous correspondence between unitary Pimsner-Popa bases for M over N and “tight” representations of the linking algebra of the quantum automorphism groups of N’ and C^d (d=dim N’). Our techniques also allow us to generalize recent results of Brannan-Ganesan-Harris and Todorov-Turowska on chromatic numbers of complete quantum graphs. This is joint work with Alexandre Conlon, David Kribs and Rupert Levene.

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